Trainers have a physical job. If they are hurt and can’t ride, or can’t ride effectively, they lose income. If they become permanently disabled, they can even lose their career.
Some horse behaviors are riskier than others, have a higher chance of a human injury. And, trainers generally are more competent with some behaviors than others – and of course there is a higher risk of injury with behaviors they handle less well. (True of every rider.)
IMO based on knowing a few pro trainers personally, every pro trainer needs to define the range of horse behaviors that they are working with, and stay off horses that are beyond their risk tolerance level. Even if they do have some skills for such problems. Don’t get hurt doing something that isn’t dressage, or isn’t jumping, etc.
As a business proposition – the coldly objective point of view – risk management is about lowering the chance of a serious incident. Not eliminating it - just reducing the unnecessary chances. Just as is true of our personal riding, as well.
The “things happen” attitude is the worst thing that any pro trainer (or any rider) can have. Such an attitude greatly increases the chance of a serious accident. ‘Things happen’ when the door is open for those things to happen.
It’s not a black-and-white question. It is not a matter of either ride all of the horses, or none of the horses. It is not about riding all of the situations, or none of the situations. The smart move for all of us is to decide what we are not going to ride. Stick to our better competencies. And what doesn’t scare us. With the rest, get help, maybe instruction, maybe make an avoidance change.
It is common for owners with a horse with a riskier behavior problem to be recommended to another trainer that specializes in such a behavior problem. That is the smart move by a pro trainer, both business and personally.
When you watch the videos of trainers who do specialize in behavior problems, they proceed with due care. Not working with the problem unless they first have in place all of the safety control measures. They rarely get hurt in these situations, because they make sure of safety, for human and horse. They are specialists with resources, experience and skills that most of us don’t have.
Any risk endeavor requires observing good boundaries. Because if not, it’s likely the endeavor will come to an unfortunate premature end. When something happens that is hard to come back from.
In fact, risk management appears to be part of the OP’s concerns with what is going on in her horse life recently. Perhaps OP could take a lesson from her pro trainer’s decision not to ride this horse – a decision that I personally agree with. Say ‘no’ to the things the OP knows are less in her wheelhouse. Even just that she doesn’t enjoy.
Don’t come up with rationalizations and self-judgments to push herself into potentially adverse situations. For her greater enjoyment of her horse time.
It seems OP’s trainer has recommended a behavioral trainer - I agree with the trainer on that. Hopefully OP’s trainer steps up to help move the horse to a better suited situation, as well. OP hasn’t been specific about that.