What makes bulls and horses buck riders off their backs?

Look at a video. See that strap in the back? That's a flank strap. The animal is bucking to get rid of it. If you let them out of the chute with no rider they would buck. You notice they buck even after the rider is unseated. And those corrals full of quietly grazing horses at the rodeo? many of those are the broncs sans the flank straps.

https://www.youtube.com/watch?v=8ePPK5ppDfo

In addition (so I am told by a fellow who rode bulls about 40 years ago) some of the bulls have reputations for particular patterns of bucking. So if the rider draws a bull that he "understands" he just might have a slightly better chance than someone else would, on that same bull.

Frankly the flank strap is a instigator

Horses learn by release of pressure. Getting rid of a rider is that reward .... Most are bred for this and enjoy it.

If you ride a bucking horse out.... To the point he can be controlled he probably won't be worth a darn as a rodeo horse.

Bulls ? Pretty much the same thing. Most bulls are a little anti social anyway.

They tie their nuts up TIGHT in that strap, would make me buck too.