Good, so I'm not crazy! LOL
What about trying to shove a creature with 4-legs by something with 2? It seems like that would be harder to shove or grapple. I mean I've worked at a stables and trust me, without a harness or something, trying to control a horse is NOT easy when nervous. Of course, maybe I just sucked at Animal Handling!
I get a more nimble creature could use Acrobatics so that makes since, but I also sometimes things like shoving require a Strength saving throw instead of Strength check. Seems inconsistent.
Some animals, like the goat, have the Sure-Footed property that grant them advantage on saving throws made against effects that would knock it prone.
It's a bit odd it doesn't grant the advantage on checks as well.