"Hate crime" means an act by the criminal that would be a crime anyway, but which has, for example, racism as part of what the criminal actually did. There is no stand-alone offence of "hate crime" or for that matter "racism". And that's why what is actually being suggested is that misogyny be a factor that makes a criminal's crime a "hate crime" in the same way that is already the case for racism.
I agree with you that racism and misogyny are similar in that they are both outlooks / patterns of behaviour. Where I disagree is how you criminalise that. Crimes are very specific things. They have to be so that the law doesn't overreach and capture behaviour that wasn't intended to be caught. That is why the formula the law uses is existing crime + protected characteristic such as racism = hate crime.
See these, for example. They're very specific and defined:
-----------
Theft Act 1968 (England and Wales)
8 Robbery.
(1)A person is guilty of robbery if he steals, and immediately before or at the time of doing so, and in order to do so, he uses force on any person or puts or seeks to put any person in fear of being then and there subjected to force.
9 Burglary.
(1)A person is guilty of burglary if—
(a)he enters any building or part of a building as a trespasser and with intent to commit any such offence as is mentioned in subsection (2) below; or
(b)having entered any building or part of a building as a trespasser he steals or attempts to steal anything in the building or that part of it or inflicts or attempts to inflict on any person therein any grievous bodily harm.
Crimes Act 1961 (NZ - I chose this one as the 1861 UK legal definition of is very Victorian and wordy and the offence of murder under English law isn't defined in statute)
193 Assault with intent to injure
Every one is liable to imprisonment for a term not exceeding 3 years who, with intent to injure any one, assaults any person.
167 Murder defined
Culpable homicide is murder in each of the following cases:
(a) if the offender means to cause the death of the person killed:
--------
Misogyny......? What's captured? Misogyistic speech? Thoughts? Gestures? I can imagine everyone in the court taking off their wigs and scratching their heads. Making it a crime is up there with claims that tax avoidance can be abolished. It's not as easy as that: you're wanting the law to do something it's not designed to do.