1 Tim 2:13-14 For Adam was formed first, then Eve; and Adam was not deceived, but the woman was deceived and became a transgressor.
Firstly, it must be noted that Paul appeals to the same Scriptures of Gen 2-3 in 1 Cor 11:7-9, and most would concede that that is a context specific situation, and not a timeless teaching. Further, as Paul Trebilco and Simon Rae in their commentary on the Pastoral Epistles note, "Teaching for a particular situation is often reinforced by appeal to Scripture (see e.g. Rom. 4:21-31; Gal. 3:16-19; 4:21-31; 1 Cor 10:1-4; 2 Cor 3:13-18)."
Secondly, Eve is the perfect candidate as an illustration since the problems in this Christian community in Ephesus have to deal with women who have been deceived, and the brutal consequences of such events. Let me again quote Trebilco and Rae:
The emphasis on Eve’s deception and that she became a transgressor is a polemical response to the situation in Ephesus… [T]hrough following the false teachers, who are themselves paying attention to deceitful spirits and teachings of demons (4:1), the young widows have already turned away to follow Satan (5:15). Hence, some women in Ephesus have been deceived by Satan (4:1; see also 2 Tim 3:6-7). In this they are like Eve, who was equally deceived and became a sinner. Eve is an illustration or example therefore of what drastic things can happen when people (in this case women) are deceived. Her susceptibility to deception, and its subsequent result is thus a warning to the Ephesian women of the danger they face if they continue to follow the false teachers. Christ Marshall comments here Paul “is not expounding the inherent meaning of the Creation-Fall narratives, but selecting aspects of the biblical accounts to illustrate and reinforce his specific ethical demands for the Ephesian situation.
Trebilco has further analysed the problems in Ephesus as it relates to this community and the problems with women and the false teaching.
Since the Pastor [author of the Pastoral Epistles] makes a link between the opponents’ teaching and women in 2 Tim 3:6 and since in 1 Tim 4:1 the Pastor connects the opponents’ teaching with “paying attention to deceitful spirits and teachings of demons”, this reference to straying after Satan suggests the women have done so by accepting the opponents’ teaching. This in turn suggests that the “gadding about from house to house … saying what they should not” refers in part at least to some women spreading the opponents’ teaching. Further, 1 Tim 2:12-15 also strongly suggests that some women were promulgating the opponents’ teaching, and were among the leaders of those opposed by the Pastor … However, exhortations against the opponents are directed to the whole congregation (1 Tim 1:6ff; 4:1, 6; 6:21; 2 Tim 3:2), which suggests both men and women were involved in the teaching.
1 Tim 2:8-15; 5:3-16 and 2 Tim 3:6-7 suggest that the opponents had a considerable impact among some women, particularly younger women, and some of these women have themselves been spreading the opponents’ teaching (1 Tim 5:13; 2:11-12). The instructions given concerning women aim to counteract this so that some women are no longer key members of the opponents’ group.
In this way, we can see that the appeal to Eve in 1 Tim 2:13-14 is entirely appropriate as an illustrative paradigm from Scripture which shows the consequences of deception, the need for theological education, and the specific situation into which this is written. Just as Eve was ἐξαπατηθεῖσα ("seduced by deception"), so too other women in this Ephesian community have been ἠπατήθη ("deceived") by the false teachers.