I think what gets lost in this kind of discussion amid internut sturm and drang is the difference between female supporting and female lead roles in popular franchises / high profile stories - there haven’t been that many - it’s partly why Rey made a big impact in TFA when it came out. It’s easy to say oh but what about Leia or Hermione - there’s no argument they’re great characters but, in the films they’re known for, it’s not their story, in the sense they’re not the lead. Who is? In the OT it’s a toss-up between Luke and Han, far more Luke for me, whereas in Harry Potter the answer’s in the title.
This all ties into representation and the messages popular media sends by that - which is, it’s fine for girls to be in supporting roles, to help and enable - but lead? To invoke Mr Chlomondeley-Warner: “Look, this pretty little thing wants to drive a car, it won’t end well.” There are predecessors for the likes of Rey, but they’re few, you can probably count them on one hand across 40 years of films. But more important is the message that girls can be the lead.
Where this all goes pear-shaped is UK society, perhaps US society has it too in different form, really mixes up the messages where boys are concerned. On the one hand boys will try anything and are dead confident, however, this gets countered by an attitude that they’re trouble, irredeemable violent little bastards and incapable of developing. It’s all very ‘what are little boys and girls made of’ bollocks, harmful bollocks too for both genders, it doesn’t help anyone. It’s a safe bet that any mother with boys will have got ‘aren’t they trouble?’ line at some point. The problem is those doing this crap-stirring hide behind the idea of boys being more confident to excuse their own antics: “They won’t care about this” but that’s probably crap too. (Also linked to the ‘hapless dad’ stereotype.)
At the same time I could see the general point being made by some blokes as to being: Can’t we have something that’s ours? That’s it’s been ‘theirs’ for years isn’t going to cut much ice against the feeling that it’s being taken away, like everything else was. Again, this is a failing of both politics and society in not encouraging a sense of security in blokes’ sense of identity in the world as it is now.
Both issues are neither the fault nor the responsibility of Doctor Who to fix, but I can see why they come up in this kind of discussion.