This is different than bragging or arrogance. Bragging or being arrogant is meant to make others feel inferior. Being confident is about recognizing your own strengths, not about comparing yourself to others.
Confidence in your riding doesn't mean that you ride perfectly. It means that you recognize and own what you do well. If you can do something most of the time, you do it well. For example, if you can pick up the correct lead on your horse most of the time, it is a skill that you are good at. Can you get better? Absolutely, there is always room for improvement. But by acknowledging that your lope departures are something that you have worked hard on, and are something that you do well, you build your confidence. Every skill is important, and as you have probably figured out, each horsemanship skill you learn builds on previous skills and helps you to reach the next level in your horsemanship journey. Those good lope departures will turn into good lead changes later!
This ability to recognize and own your riding skills and abilities is key to developing your confidence. By recognizing these skills that you have worked to develop, you show yourself that you can learn, improve, grow, and overcome challenges. All of these build confidence!
So when someone compliments your riding, if you downplay or dismiss the strength that they have recognized in you, you are telling yourself that you don't have that riding skill. This subconsciously erodes your confidence!
To help you to recognize your riding strengths, write down a list of your top 10 riding skills.
They can be simple things, like, I can saddle my own horse, or I can lunge my horse at all gaits and keep him under control, or I can jog on a loose rein. They might even be skills that you take for granted, but they probably are skills that you have spent a lot of time learning and developing.
If you need help coming up with 10 riding skills, ask your trainer or a riding friend what you are good at.
And when they tell you, smile, say "thank you," and then shut your mouth.