I think explaining your expertise is not arrogance. Rather, it helps laymen understand the value of your expertise. Imagine if you ask the plumber working on your pipes “How do you do that so well” and he says “It’s really easy, anyone could do it” because he doesn’t want to brag about all the training and experience he has under his belt.
Comes time to pay the bill, you’ll be wondering why he gets $1200 for something so easy.