ime, in the NT, your trickiest problem is in 1 Timothy 2 -
Likewise, I want women to adorn themselves with proper clothing, modestly and discreetly, not with braided hair and gold or pearls or costly garments, but rather by means of good works, as is proper for women making a claim to godliness. A woman must quietly receive instruction with entire submissiveness. But I do not allow a woman to teach or exercise authority over a man, but to remain quiet. For it was Adam who was first created, and then Eve. And it was not Adam who was deceived, but the woman being deceived, fell into transgression. But women will be preserved through the bearing of children if they continue in faith and love and sanctity with self-restraint.
The whole passage is fairly hairy, in terms of equality, but the bolded parts are the really sticky bits.
The only answers I've ever seen to them has been to dismiss them as extra-biblical, hypercontextualize them by saying they were about a very specific woman, or suggest that Paul was responding to a question put to him.
All of which seem reather convoluted to me. But this is the passage which has been used to clobber me the most, and the one I find the hardest to deal with.