If we consider the Bible itself as a "source," there are several principles that connect with 1 Timothy 2:11-12 relative to the role of women in comparison to that of men.
Civil Leadership
No woman in the Bible is ever established by God in a leadership position over His people. There were women leaders. Athaliah was a queen reigning over the people of Israel for a time. But she is depicted as an usurper, the granddaughter of Jezebel, and not one who worshiped or feared God.
Many will object and say that Deborah was a judge. Be careful. Deborah was a prophetess. According to the Biblical record, there is no clear indication that this was either of God's choosing, or of Deborah's own choice, that she judged the people: the people appear to have come to her and made her their judge.
4 And Deborah, a prophetess, the wife of Lapidoth, she
judged Israel at that time.
5And she dwelt under the palm tree of Deborah between Ramah and Bethel
in mount Ephraim: and the children of Israel came up to her for
judgment. (Judges 4:5, KJV)
Prophethood
Women were prophetesses. Miriam, Deborah, Huldah, Noadiah, and Anna are specifically named. Prophets are not leaders by virtue of their status as prophet. They simply speak for God. The commands given by a prophet are recognized even by the kings who are their superiors to have originated, not with the prophets themselves, but with God. Even a donkey prophesied, and, of course, donkeys are not to be considered our leaders.
Priesthood
God ordained men as priests. In God's order, there were no priestesses. Priests served as spiritual leaders for the people, and were also their teachers. They established schools and taught the people from them. Samuel's schools were well known. There is no Biblical record of a woman teaching in any of these schools.
Bishops and Deacons
At the death of Christ, the system of Levitical priesthood was ended. A new gospel order was established in the Christian church. Directions were given that bishops (churches today might say "elders") and deacons must be men who ruled well their own households, were married to one wife, etc. (See 1 Timothy 3.) Women are excluded by these specific criteria. The New Testament order maintained male spiritual leadership of the church.
Deaconesses
Those who want women as leaders will often look for hooks upon which to hang their opinions. Phebe, mentioned in Romans 16:1 as a servant of the church, variously translated as "minister" or "deaconess", is sometimes used in this unending debate, and more significantly, Junia/Junias of Romans 16:7, whom many claim was a woman, and whom Paul calls an "apostle."
Salute Andronicus and Junia, my kinsmen, and my fellow-prisoners, who
are of note among the apostles, who also were in Christ before me.
(Romans 16:7, KJV)
But there are considerable difficulties with assuming Junia/Junias was a woman. First, there is that troublesome "kinsmen." Greek scholars may say that even though this is in masculine plural form, that form would also be used to address a mixed group. But more importantly, there is that mention of "my fellow-prisoners" which invites the searching question: "Were women imprisoned with men?"
At the very least, there can be no certainty to the claims that Junias/Junia was indeed a woman. True, if Junia was a woman, and an apostle, it would be precedent-setting. However, it is imprudent and unwise to establish a Biblical doctrine upon mere suggestions, without solid evidence.
Analysis
Prophets speak. And they speak to groups of people as well as to individuals. Prophetesses, who are speaking at God's bidding, may most certainly do so in the church or anywhere God asks. The prophetic word, however, is not their own--it is God's. It is not the prophet or the prophetess who is teaching via the inspired word, but God Himself.
Joel 2 indicates that women will receive the spirit of prophecy as well as men.
28 And it shall come to pass afterward, that I will pour
out my spirit upon all flesh; and your sons and your daughters shall
prophesy, your old men shall dream dreams, your young men shall see
visions: 29 And also upon the servants and upon the
handmaids in those days will I pour out my spirit. (Joel 2:28-29,
KJV)
Inasmuch as a woman may speak for God, as a prophetess, her privilege of speaking in church or in a secular environment cannot be denied based on scripture. Is she teaching? Perhaps. Though we acknowledge the authority behind her inspiration to be that of God (assuming she is a true prophet).
But there is no scripture in support of having a woman as a leader, either in the church or in the civil realm, who is in the position of personally making decisions and having authority. Biblically, this principle holds true of both civil leadership, and spiritual leadership.
NOTE: The Biblical age at which one left childhood and became an adult was 20. There is no scripture that forbids a woman from having authority over children, which would mean having women teach high school students, who are generally under 20, should not conflict with any Biblical passage.
Waggoner's Explanation
There is also an interesting essay on the question published in 1887 (not exactly the days of the first apostles, by any means, but interesting for its historical perspective coming from a pre-women's-suffrage era) by a Mr. Ellet Waggoner. He addresses multiple Biblical texts on the topic, including the passage in 1 Timothy.
The question on the text itself is worthy of consideration, for many
good people think that the Bible forbids women to take part in public
religious service. 1 Corinthians 14:34, 35, reads as follows:-
“Let your women keep silence in the churches; for it is not permitted
unto them to speak; but they are commanded to be under obedience, as
also saith the law. And if they will learn any thing, let them ask
their husbands at home: for it is a shame for women to speak in the
church.”
It is worthy of mention that those who are most bitterly opposed to
women’s taking part in public service, are inconsistent with their own
interpretation of this text. They interpret it to mean that women
should never speak in public, either to preach, or to bear testimony
in prayer-meeting; yet there is not a church in the land which does
not have women singers, and in many of them the singing would greatly
languish if it were not for the women. Now it is certain that those
who sing do not “keep silence.” We do not think that this is wrong,
not a violation of Paul’s injunction; we cite this instance merely for
the purpose of showing the inconsistency of those who interpret Paul’s
words as prohibiting speaking in meeting, but allowing singing. Now if
the injunction to “keep silence” does not prohibit singing, it is
reasonable to suppose that it does not prohibit speaking at proper
times and in a proper manner, for simple speaking is far more nearly
an approach to silence than is ordinary singing.
And this we shall find to be the case, when we consider a few other
texts; for we must always let scripture explain scripture. Read the
other text to which our correspondent referred, 1 Timothy 2:11, 12:
“Let the woman learn in silence with all subjection. But I suffer not
a woman to teach, nor to usurp authority over the man, but to be in
silence.” This must certainly be considered as parallel to, and
explanatory of, 1 Corinthians 14:34, 35. But there is nothing in it
which would stop a woman from bearing testimony in social meeting, or
even from preaching. Notice that Paul says: “I suffer not a woman to
teach, nor to usurp authority over a man,” the idea being of a women’s
setting herself up as superior, and assuming authority which does not
belong to her. But a simple testimony for Christ is the farthest
removed from the assumption of authority, and even the preacher who
usurps authority over his hearers, is out of place. The place of the
preacher is not to be a lord over God’s heritage, but to act the part
of an ambassador for Christ. From the two texts quoted we must
conclude that Paul did not mean to prohibit women from witnessing
publicly for Christ, but only to have them act with becoming modesty.
This conclusion is made positive by other texts. In 1 Corinthians
11:4, 5, 13, the same apostle says: “Every man praying or prophesying,
having his head covered, dishonoureth his head. But every woman that
prayeth or prophesieth with her head uncovered dishonoureth her head;
for that is even all one as if she were shaven.” “Judge in yourselves;
is it comely that a woman pray unto God uncovered?”
In these verses, and the context, the apostle is giving directions for
the proper conducting of public worship. Now if in chapter 14 he meant
to teach that women should utter no sound in public service, why did
he here give directions concerning their praying and speaking in
public assemblies? Certainly no directions are needed for the
performance of that which is forbidden, and the fact that Paul tells
how women should pray and prophesy in public meeting, shows that such
action was not forbidden.
To forbid women any of the privileges of the gospel would be utterly
at variance with the spirit of the gospel. Says Paul: “For as many of
you as have been baptized into Christ have put on Christ. There is
neither Jew nor Greek, there is neither bond nor free, there is
neither male nor female: for ye are all one in Christ Jesus.”
Galatians 3:27, 28. That means that in the gospel plan there is no
difference made for race, condition, or sex. A woman stands before God
a sinner, just the same as a man; she is responsible for her own sins,
and, if saved, must be saved in exactly the same way that a man is. No
Christian would think of prohibiting a person from taking part in
meeting, on the ground that he is a servant, or because he is of a
different nationality from the majority of the members of the church;
then no Christian should prevent a person from speaking to the praise
of God, because that person is a woman.
To interpret Paul’s language in 1 Corinthians 14:34, 35, as meaning
that women should bear no part in public worship is to do violence to
the Scriptures which, being inspired, must always and everywhere be
harmonious. Thus in Acts 21:8, 9, we read that Philip the evangelist
“had four daughters, virgins, which did prophesy.” Paul speaks of
Phebe, “a servant of the church which is at Cenchrea” (Romans 16:1),
and in Philippians 4:3 bespeaks the care of the church for “those
women which labored with me in the gospel, with Clement also, and with
other fellow-laborers.” And the mighty and eloquent Apollos was
instructed in the way of God by Aquila and his wife Priscilla. Acts
18:2, 24-26.
In the Old Testament we read of “Miriam the prophetess” (Exodus 15:20)
by whom the Lord spoke as well as by Moses and Aaron (Numbers 12:1,
2). We read also (Judges 4) of “Deborah, a prophetess” who judged
Israel, and whose wisdom and prudence were esteemed so highly that
Barak would not go to war without her counsel and her presence. Still
later we read of “Huldah the prophetess” (2 Kings 22:14) to whom
Josiah sent when he would inquire of the Lord concerning the book of
the law which the priest had found. There is something remarkable
about this case. At this time Jeremiah had been prophesying for five
years, yet the king sent to Huldah instead of to him. Moreover the
king’s messengers to the prophetess were, among others, a scribe of
the law, and the high priest, whose lips should keep knowledge, and at
whose mouth men were accustomed to seek the law. Micah 2:7. Yet it
seems that on this occasion no one had the word of the Lord except
this woman.
We have considered this
matter at this length not only for the satisfaction of our
correspondent, but also to meet a very common infidel cavil. There are
many men, and more women, of a class who seek to overthrow the
divinely-established order of nature, who are accustomed to rail at
the apostle Paul as a crusty old bachelor and a misogynist, because of
his words to the Corinthians. Hastily assuming that he absolutely
forbade women to take any part in public meetings, they think that the
present liberty accorded to women is an evidence of the advance which
people of the nineteenth century have made over Paul’s antiquated
notions. From railing at Paul they naturally come to despise all his
writings, and as a natural consequence, they lightly esteem the entire
Bible.
But Paul was not crusty, he was not a misogynist, and he was not a
bachelor. He was a large-hearted, whole-souled, loving Christian, who
treats of the family relation with a knowledge and tenderness not
exceeded by any writer who ever lived. Instead of commanding women to
say nothing in meetings for the worship of God, he encouraged them
even to occupy responsible positions. What he did do was to give
instruction that would keep them from being classed with the heathen
women who, in their eagerness for notice, divested themselves of that
modesty which always characterizes true woman, and which the gospel
tends to heighten. (Waggoner, Signs of the Times, May 12, 1887)