Here's an article from Australia, because animals suffer the same south of the equator.

What are the animal welfare issues with rodeos?

A rodeo is a form of entertainment or sport where horses and cattle are used to demonstrate riding and handling skills. Events include bronco riding, bull riding, calf roping, team roping and steer wrestling. The RSPCA is opposed to rodeos and rodeo schools because of the potential for significant injury, suffering or distress to the animals involved. Based on observed behaviour, there is very little evidence that the animals ‘enjoy’ the rodeo experience. Rodeos are held in all states and territories in Australia except for the Australian Capital Territory where they are prohibited.

Bronco and bull riding

Rodeo horses and bulls buck repeatedly as an instinctive reaction to being repeatedly kicked with metal spurs and to the tightened flank strap around their sensitive underbelly. Horses and cattle are prey animals and their reaction to being ridden in this way is the same as their reaction to being attacked by a predator, a situation where they experience increased fear, stress and panic. It is not uncommon to see horses and bulls hurl themselves at solid objects in order to rid themselves of the rider. Only when the rider has been thrown or dismounts and the flank straps loosened do they quieten down. Also, some ridden animals are so distressed that they then charge the rider on the ground, further demonstrating this very strong fear response. A study of bull behaviour at rodeos determined that nearly one third of animals assessed showed signs of distress leading up to the start of bull-riding events and that those who did not react may have either become habituated to the aversive situation or have given up and endure the negative experience [1].

 

 

https://kb.rspca.org.au/knowledge-base/what-are-the-animal-welfare-issues-with-rodeos/ 

 

Further:  The article goes on to discuss calf roping, steer wrestling and team roping, with several gruesome photos. To cap it off,

What you can do

All rodeo events will cause stress, fear and pain as well as injure animals for the sake of sport and entertainment. Subjecting cattle and horses to these experiences is not justified. You can help stop rodeos by raising awareness of the risks to animals inherent in rodeos, especially if a rodeo is held in your local community. You can also meet with your local member of parliament and write to the Minister responsible for animal welfare in your state/territory to urge rodeos to cease.

 

 

That's it, contact your local and state politicians.  Give them some bad press for not doing something, because they sure won't be moved by anything else. Circuses are gradually cutting out animals, let's shut down the rodeos too.

Troglodytes.