R. Simeon can be challenged on the basis of:
Nu 30:12 But if her husband hath utterly made them void on the day he heard [them; then] whatsoever proceeded out of her lips concerning her vows, or concerning the bond of her soul, shall not stand: her husband hath made them void; and the LORD shall forgive her.
Since her vow may be nullified without her consent by her husband, his argument has no basis.
Nevertheless, this answerthis answer, that she may have said things or thought things which were inappropriate, may be a good inference from 'just as she is unclean during her monthly period.' Some women, certainly not my wife... dear, may be prone to saying things during that time which are inappropriate as well.
However, there are other scriptures which may speak to the issue:
Le 12:2 Speak unto the children of Israel, saying, If a woman have conceived seed, and born a man child: then she shall be unclean seven days; according to the days of the separation for her infirmity shall she be unclean.
Le 12:5 But if she bear a maid child, then she shall be unclean two weeks, as in her separation: and she shall continue in the blood of her purifying threescore and six days.
If the child is a male she is unclean for a week, if a female for two weeks. The male has somehow redeemed his mother from a week of un-cleaness.
In Sensus Plenior, a Christian hermeneutic where Jesus is always the answer, when there are two things, one is earthly and one is heavenly representation of the same thing. For a female child, the woman is unclean for a week in the flesh and a week in the spirit. But for the male, she is only unclean in the flesh since it is the seed of the woman who will bruise the heel of the serpent. And she is 'saved' through childbearing. The male son is a shadow of Christ.
1Ti 2:15 Notwithstanding she shall be saved in childbearing, if they continue in faith and charity and holiness with sobriety.
The same sacrifice is made for a male or a female child, which is for the uncleaness shared in the two circumstances. Is the sin covered by the son a spiritual uncleanness or a physical one?
Ps 51:5 Behold, I was shapen in iniquity; and in sin did my mother conceive me.
Since God commanded man to multiply, and this is done through conception, the act is not sin. This must refer to the sin nature (or evil inclination) that is passed to us genetically. Therefore the sin that remains uncovered, and requires a sacrifice is the spiritual sin. Both males and females must be born again.
The sin offering is given for the sin of passing the evil inclination on to the child and causing a little one to stumble. It is a sin of the flesh, not of intention.
God desires spiritual children. The issue of blood without conception is a similar un-cleaness in that it is a symbol of not being fruitful and multiplying spiritually. It is a sin of the flesh, not of intention. This is why being barren was such a disgrace.
The direct answer to the question is Yes. We are not supposed to pass our sin nature to our children, but we do. It is a sin of the flesh, not of intention. It is a sin covered by the cross. Our responsibility, as part of our repentance is to 'train them in the way they are to go'.