I have learned that communication and empathy between men and between women are very different. Other genders tend to have more complex dynamics.
I think women communicate their empathy more openly. Men usually hide their empathy in gestures or phrases. And I think it's really hard to show empathy as a man and still "conform", and as an outsider it's hard to understand the way men show empathy.
That said I think you are right to some degree (although there is a better way to phrase it, hence the down votes), you are kinda limited in how much empathy you get from men because of the way they communicate. And if they show more, their non-conformity can pose a social risk that can be dangerous to their social acceptance / standing, although I might be speaking from my own perspective here as an AuDHD guy. Turns out when you have autism you are a walking risk so learning this is just a matter of time and risk is baked into every social interaction.
What I'm trying to say is: I think you are right, I think the reasons are very complex but I think bro culture needs an upgrade in that regard.