Why do our angel fish butt heads?

We have two angels, and they like to float motionless facing each other, then accelerate toward each other till their “faces” bump. Then they back up, float for a few seconds, and do it again. It doesn’t seem to be particularly hostile, and they aren’t injuring each other. So what on earth are they doing?

Establishing their territory. You apparently have two angels of the same sex. Or, perhaps one was introduced to the tank before the other one? Angels do this if one is even the slightest bit bigger, to establish dominance/territory. As long as they are not actively fighting and ripping each other to shreds, they should be okay. If it really bothers you for them to do this, try re-arranging the items in the aquarium. They will think they are in a whole new place and may stop fighting altogether.