It is certainly inappropriate and unprofessional. But it's also sexism, in that for centuries men here have been using power to push women to have sex without regard to their actual interest. E.g., marital rape didn't become a crime across the US until 1993: https://en.wikipedia.org/wiki/Marital_rape#United_States

That isn't sexism, similar things happens all the time in gay relationships. Similarly men murdering women in relationships is not sexism, since gay men murder their partners at a higher rate than straight men. So it isn't sexism, it isn't about men hating women, it is just about men committing a lot more brutal violence on average. Or in this case, it is just about men being a lot more forceful about sex than women, even when they are proposing to men.

The notion that the law allowed men to rape certain women seen as their property isn't sexism?

You could be right that men have some innate tendency to commit more violence. But what they also have, as your excuses here make plain, is more social license to commit violence. The former, if true, is just a fucked up fact our evolutionary history. The latter, though is very definitely sexism.

Propositioning a woman who you manage at work is sexual harassment and sexist.

Sexual harassment? Sure. Sexist? Sorry, no, that's just silly. By your logic, if a male manager only propositions female subordinates, it's sexist, because he isn't also propositioning male subordinates. That's not sexist, that's a side effect of the male manager being heterosexual.

By your logic, every person that only dates people of a particular sex is "sexist", which is completely ridiculous.

You're thinking that I label the behavior sexist because the manager propositions only women and not men. I am not. I am labeling the behavior sexist because it contributes to both a work culture, and the wider culture, which excludes women from status and power.

I don't know about this; it isn't completely unheard of for female managers to proposition male subordinates, it just doesn't happen as often obviously. I think it's wrong and abusive, no matter which sex does it (and to whom; (gay) men propositioning other men happens too), but I have a hard time seeing how this is "sexist" or only harmful to women, though obviously, due to inertia I think (more men being in positions of power), it negatively affects women more. I will grant you, however, that it can be argued that it contributes to keeping the gender-unequal status quo.