This looks like a use of the archaic meaning of suffer, which was 'tolerate' or 'allow'. If it's in a very old text, I'd understand the first to mean something like 'I won't tolerate a woman' and the second "I won't tolerate a woman teaching" or "I won't allow a woman to teach".
NB Many people who aren't aware of this old usage know the biblical phrase "Suffer little children" and presume it's about children suffering. They don't realise that the full phrase is "Suffer little children to come unto me", which means 'Let them come'.