Here's an interpretation from a vegan lens (apparently P!nk isn't a vegetarian but tries to be plant-based when possible):

Using cow's milk to feed human babies is as artificial as using human mothers' milk to feed a cow. Much of the video is a commentary about how outside forces (like the sumo opponent) try to force us to accept an unnatural reality.

I hadn't seen the video before. It's quite good--matches the song well in style and visuals.