1 Timothy, Chapter 2 vs 7 was the one that suggests to me Paul deigns all his writings infallible.
"I speak the truth in Christ, and lie not."
And although I can agree with the slant you take on the Corinthians verse, further on down in Chapter 2 of 1 Tim Paul says:
I suffer not a woman to teach,....
I still can't shake the idea that he just plain doesn't like women. Suffer is a strong word. I realise that men are given authority over their wives, and a lot of his teachings about women do make good sense, albeit standing against modern culture, but he still seems like a misogynist to me.