Why Complementarians are Wrong about 1 Tim 2:12

I recently participated in a conversation about Women in Leadership, and the focus was on Women in the New Testament, and especially 1 Timothy 2:12. 

During the discussion I noticed something that I've not realised before.  Paul's injunction, I am permitting no woman to teach or to dominate a man, is a blanket statement with no exceptions provided.  This is not the way complementarians understand this verse.  Complementarians understand this verse to mean that women are not allowed to teach men, but ἀνδρός, is a separate part of the statement relating to αὐθεντεῖν, and Paul does not say that women are not allowed to teach men, but rather that they are not allowed teach, as well as not being allowed to dominate men.

We are stuck with two options.  Either this blanket prohibition forms a contradiction with a passage like Titus 2:3, where women are to teach what is good (καλοδιδασκάλους); or we understand that this is a contextually determined statement, and the women are not to teach in this situation because they are part of the problem of spreading heresy (1 Tim 5:13-15; 2 Tim 3:6), and thus they are instructed to learn (μανθανέτω). 

The more I read the Pastoral Epistles, the more I am convinced this is a highly contextual letter, and attempts to read it without reference to the socio-historical context are dangerously misleading.