When taking my first analysis class I was sure it is no coincidence the word begins with anal.

I'm going to steal that line, if you don't mind. :-)

It took a while for me to develop habits of skepticism about things that seem obvious at first glance. That's the attitude I think he is describing.

Yes. The attitude of "I don't care if this looks right; am I absolutely certain that it is right, in all possible universes consistent with my axioms".