I've read a couple of articles by nationally known trainers discussing the need to find the right horse. There is truth in the statement that you should find the right horse. Just because a horse works well with one person, doesn't mean it is going to work well with everyone. Horses, like humans, have personalities and sometimes the personalities are a good match and sometimes not. The issue is to not get confused and hung up on the concept of the perfect match.
One of the most common situations I get involved with relates to a horse and rider who do very well together in the arena, but out on the trail the horse gets spooky and the rider can't deal with it. Then the owner decides that the horse is not right for them. From my perspective, since the horse does well in the arena, it probably just needs training to get accustomed to the trail. We get a lot of horses in here that do very well in the arena but are not safe on the trail. For example, a reining cow horse or a reiner don't usually get out on the trail, when they do go out, they are likely to be spooky. I have never seen any horse, no matter how well trained, that couldn't benefit from some type of training. De-spooking is one of the areas we spend a lot of time on.
Another thing I see a lot is that people seem to tolerate a lot from their horses. Sometimes this is because they don't know any better. Through a lack of knowledge we accept behavior that can be dangerous and should be corrected. For example, I went to work with a horse that refused to cross a stream. As I rode down the trail, the horse began to buck. I dealt with the bucking and proceeded on to the stream. The horse learned to cross with little trouble and the lesson was very successful. When I returned, I told the owner about the bucking. His response was that the horse just always does that but he gets over it quickly. We don't have to accept, and we should not accept, bad behavior, whether in the arena or on the trail. Before you sell your horse because you think your personalities don't match, consider what the problems are. Just possibly, training is what needs to happen. This includes training for you as well as the horse.
There are also horses that do great on the trail but are hard to control in an arena. This is often because the horse does not understand the exercise or the maneuvers that we sometimes do in the arena. Here, again, this is a training issue for the horse as well as the rider. While most exercises we do in the arena can be done outside, performing certain maneuvers in a more confined space may take some getting used to. Arena work is more specific and the rider needs to be clear and consistent with his or her cues.
There truly are situations where the personality of the rider and that of the horse just do not fit. However, my thought is that before you sell your horse and go looking for that perfect match, spend some time with a trainer to get your horse accustomed to the trail or comfortable with arena work. You may find that you already own the perfect horse.