Two observations:
People who have a joke about universities and a bit of a tease about it aren't necessarily immature. It seems a bit over the top to suggest some ribbing is immature, it's completely mature.
It hardly seems a bad thing to have some university rivalry and the jokes that go with it. I'd argue that it's a good thing, because it helps people to feel like they belong to something and is generally quite funny. It'd be just weird going to Cambridge or Oxford in the UK and not getting a few shots in on the other, so I cannot understand why in Australia, where being a dick head like that is practically wound into our culture, that everyone gets so upset because someone said UniMelb is snobby, or that Monash is full of people who want to go to Melbourne. Relax guys.