Not something the UK Justice Secretary understands
https://inews.co.uk/news/politics/dominic-raab-called-out-bbc-presenter-misogyny-men-women-1234742?ito=twitter_share_article-top
Raab is clearly an idiot in not recognising that misogyny is a term that applies to hatred or contempt towards women or girls. However there are some broader issues that are relevant in terms of whether or not the scope of hate crimes should be extended.
The first is that misogyny, in its definition is not necessarily about men demonstrating contempt for women, its definition also applies to circumstances (perhaps rather rarer) where women demonstrate contempt towards their fellow (excuse the gendered term) women.
Also were hate crimes to be extended then presumably it would follow the same approach currently adopted but add an additional 'protected characteristic' from Equalities legislation. In this case that would be sex - so a new hate crime would apply to any circumstance where an individual has:
1. demonstrated hostility based on sex or
2. been motivated by hostility based on sex
So this would apply not just to hostility towards women by men under those definitions, but also women towards men etc. And while it can be argued that the former is much more common than the latter, from the perspective of an individual person the impact of that hostility may be just as negative and therefore as deserving of protection under hate crime legislation.
The analogy is that there is legislation on hate crimes based on race - they don't just apply to hatred from white people towards ethnic minorities but also apply similarly under circumstance where hatred is directed towards white people from ethnic minority groups or individuals.
So I suspect that any extension of hate crimes (not that Rabb nor Johnson appear to want it) should be on the basis of sex, rather than only protecting women from hatred from men.