I think it's interesting that the lack of men in primary teaching gets mentioned in the context of things men are obliged to fight for, as if there's been a historical precedent of men being excluded from the profession, which we're only starting to redress. Or as if the applications and assessment process has been biased against men, with their achievements given less weight and their future performance assumed to be lower than that of women. Or as if the workplace 'feminised' to an extent to which they feel unable to function there: harrassed, isolated, not taken as seriously as their female peers.
As far as I know, there was a majority of male primary school teachers in the post-war period. They were paid more than their female colleagues (because they'd have families to support) and women were expected to leave the profession upon marriage (because they'd have families to support). 'Talk and chalk' teaching was encouraged, as was rigorous discipline and very structured learning. Equal pay became more of an issue in the sixties, and that's when the gender imbalance shifted the other way.
Today, it's not the case that the primary school environment is hostile towards male teachers. The opposite: they're welcomed by parents and children, they're assumed to have leadership ambitions, they're 'presumed to be competent and confident in many elements of their practice, which may need to be 'proved' more demonstrably for female teachers' (quote from a male primary teacher).
The sticking point seems to be that this is seen as a women's profession, and therefore is lower prestige and an incongruous (even charitable) choice of field for a man to enter. And that's not women's fault. Nor is the toxic masculinity culture that classifies any job which involves nurturing, young kids, or mopping up snot and tears as a woman's thing.
I think it would be great if there were more male primary school teachers, but I don't understand why it invariably crops up on feminism threads as a counterpoint about the struggles men face. It's not women keeping men out of primary school teaching. The solution is effectively a PR campaign in which we seek to persuade would-be male teachers to overcome their reservations about entering a field which is suspiciously full of women and must therefore be lower-level. 'Men, come along! We promise this isn't just for ladies, and is therefore worthy of your consideration!'