Wife & confidant aren't a problem. I think every president has gotten some advice from his spouse during pillow talk or over breakfast.

The problem people have with Hillary is that she seems like more of the "puppet master" type. She has the calculating vibe of someone who pushed her husband into the highest office and exerted unparalleled influence over his policies. It seems like she had planned to use the Bill Clinton presidency as a stepping stone to fulfill her own dreams of being the first woman president from before she even married Bill... that she put up with his infidelities and party guy image because he was a pawn in her strategy, and she was cold enough to not need a real lover.

I'm not saying any of this is true. It is probably much more complicated than all that. But that is how it looks to many people. Thus, in this context, "co-president" has a bad taste. Historically, this was fairly common with kings & queens. England & Holland are both ruled by Queens now because of the strength of those particular women and the flimsiness of the men around them. It reminds me of the Egyptian female pharaohs Hatshepsut and Cleopatra. Women like that tend to scare the shit out of men and other women alike...