On some level, you're describing a difference between traditional male bonding (joking and "razzing") and traditional female bonding (being kind and supportive). Both of these can be positive and both can be toxic - bullying is an obvious case, but just ask anyone who has been in a supposedly "supportive" environment filled with backstabbing and gossip how nice that is.

I don't know why there's a need to define either of these as inferior and wrong - isn't the point of diversity to allow people from different backgrounds to take different approaches?

To me, personally, the "kind, supportive" style often comes off as insincere. It's actually a barrier to me trusting someone. But I don't know, maybe that's just me.