There's a LOT of reading between the lines going on, here. Going from Matt doesn’t feel comfortable around you. He’s worried that you either don’t like him for some reason, or you’re mad at him. He thinks maybe you’re upset about his recent promotion, because it means you’ll have to do more work to cover for his newfound absence on the team to What we’re really saying here is that your unreconcilable feelings toward…
So, this is subtle, because everything you say is good advice and can't really be argued against. Calm down, don't overreact, give the benefit of the doubt, be constructive, etc, etc. These are basic, undeniable principles of good human interaction. But. But . Consider an alternative hypothesis; that the author really did experience a bit of nasty, petty sexism. In that case, responses like yours at best sweep the pr…
Actually, I'd say GPs advice is the right course of action, in part precisely because real sexism might be involved. In addition to providing a productive way forward if that is not the case, it also avoids an overreaction which provides an excuse for (and thus masks the sexism of) any adverse action in the future.
It doesn't sweep anything under the rug, in fact, it is the best approach for bringing what is actually happening out in the open (rather than escalating the one clear, undebatable problem in the situation under discussion, which is that people are acting based on unsubstantiated assumptions about others motivations.)