Before we compare the two verses, we should first determine the original message and context given when they were written.
» [1 Timothy 2: 9-16] (NASB)
9 - Likewise, I want women to adorn themselves with proper clothing, modestly and discreetly, not with braided hair and gold or pearls or costly garments,
10 - but rather by means of good works, as is proper for women making a claim to godliness.
11 - A woman must quietly receive instruction with entire submissiveness.
12 - But I do not allow a woman to teach or exercise authority over a man, but to remain quiet.
13 - For it was Adam who was first created, and then Eve.
14 - And it was not Adam who was deceived, but the woman being deceived, fell into transgression.
15 - But women will be preserved through the bearing of children if they continue in faith and love and sanctity with self-restraint
» [Romans 5: 11-17] (NASB)
11 - And not only this, but we also exult in God through our Lord Jesus Christ, through whom we have now received the reconciliation.
12 - Therefore, just as through one man sin entered into the world, and death through sin, and so death spread to all men, because all sinned—
13 - for until the Law sin was in the world, but sin is not imputed when there is no law.
14 - Nevertheless death reigned from Adam until Moses, even over those who had not sinned in the likeness of the offense of Adam, who is a type of Him who was to come.
15 - But the free gift is not like the transgression. For if by the transgression of the one the many died, much more did the grace of God and the gift by the grace of the one Man, Jesus Christ, abound to the many.
16 - The gift is not like that which came through the one who sinned; for on the one hand the judgment arose from one transgression resulting in condemnation, but on the other hand the free gift arose from many transgressions resulting in justification.
17 - For if by the transgression of the one, death reigned through the one, much more those who receive the abundance of grace and of the gift of righteousness will reign in life through the One, Jesus Christ.
The passage in Timothy is regarding instruction to a Christian woman and their role within the church and home. The passage in Romans 5 is regarding the importance of Justification and how it was NECESARY for sin to take place in the purpose of God's plan to reveal Himself to His elect (people He predestined to go to heaven).
Now that we have a broader sense of the context of each passage we can exegete certain verses to build up premise to what the answer actually is.
» [1 Timothy 2: 9-16] (NASB)
13 - For it was Adam who was first created, and then Eve.
» [Romans 5: 11-17] (NASB)
14 - Nevertheless death reigned from Adam until Moses, even over those who had not sinned in the likeness of the offense of Adam, who is a type of Him who was to come.
Adam was a type of Christ.
»[1 Corinthians 15: 45 - 49] (NASB)
45 - So also it is written, “The first MAN, Adam, BECAME A LIVING SOUL.” The last Adam became a life-giving spirit.
46 - However, the spiritual is not first, but the natural; then the spiritual.
47 - The first man is from the earth, earthy; the second man is from heaven.
48 - As is the earthy, so also are those who are earthy; and as is the heavenly, so also are those who are heavenly.
49 - Just as we have borne the image of the earthy, we will also bear the image of the heavenly
Headship: Bringing everything together
The main reason why sin came into the world through Adam and NOT Eve, as specifically spelled out in the bible, is because of a theme ordained by God known as headship. It can be found in 1 Corinthians 11 and Ephesians 5. Basically, through this set order of things, God is the head of Christ, Christ is the head of the church (the elect) and a man is the head of his wife. The most simplistic definition of federal headship can be found at http://www.monergism.com/topics/federal-headship. Through this ordained order, we all come under sin because of Adam (Eve came from Adam but Adam was first). To get caught up on the particularities of the actual order of operations with regards to the fall of man, is to fundamentally miss the concept of headship, which, I admit, is not so quickly comprehended but can be understood by studying the above passages of Scripture.
Lastly, if you want to study this further, please consider:
»[Genesis 2: 23 - 24] (NASB)
23 - The man said, “This is now bone of my bones, And flesh of my flesh; She shall be called Woman, Because she was taken out of Man.”
24 - For this reason a man shall leave his father and his mother, and be joined to his wife; and they shall become one flesh.
25 - And the man and his wife were both naked and were not ashamed.
☼[1 Corithians 11: 1 - 2] (NASB)
1 - Be imitators of me, just as I also am of Christ.
2 - Now I praise you because you remember me in everything and hold firmly to the traditions, just as I delivered them to you.
3 - But I want you to understand that Christ is the head of every man, and the man is the head of a woman, and God is the head of Christ.
Thank you for reading.
Alex
►Sources:
www.biblehub.com
www.gotquestions.org/Jesus-second-Adam.html
www.studylight.org/lexicons/greek/gwview.cgi?n=177
www.monergism.com/topics/federal-headship