What exactly is a misogynistic man?

I’m not sure what you think homosexuality has to do with misogyny. Men don’t have relationships with other men because they hate women.

Donald Trump is a good example of a misogynist (as well as an ass).

As to your question about a “normal relationship”, that depends on what you consider normal. Personally, I don’t find being in a relationship with someone who does not value and respect me for who I am rather that what I look like, normal.

You can’t always tell, right away, and being misogynistic has nothing to do with being gay.
These are men that for, whatever reason, their upbringing, past bad experiences with women, machismo, view women as inferior.. They have o problem exploiting and abusing them sexually or otherwise and view females as objects to be used for the males ego and genital gratifications.
Misogyny is a shape shifter and manifests in many forms from base chauvinism to outright abuse.