Egos should definitely be left at the door.
However, given that we are the professionals, I would say “bragging” and “informing” a client are very closely related. Having an understanding of the human body as well as experience in the gym is what people want you to have as you are selling yourself.
You dont want to hire a trainer that says “Yea, I know a little about the gym”.
People want to hire a trainer that is capable of pushing them to their limits, get results, but do so in a way that is not dangerous. The only way to get that impression across is to tell them.