There are many people out there who will say that if you havn't made Parkour your lifestyle, then you arn't doing Parkour. I think that may be a little harsh, especially to someone who is just learning it, but the idea is still there, and we should strive for that.
As far as your brother is concerned, or anyone else for that matter, there really isn't anything you can do. He's gonna believe whatever he wants. However, I would like to point out one thing. Comparing Parkour to "other sports" is like comparing apples to rectangles. "Other sports" are about competition, and being better than someone else at something. We are pushed into this mode of thinking all our lives. Hell, there are even speed events for climbing Mount Everest now!
We are trying to grow in a world filled with X-sports, and while much of what we do can be considered extreme, the adrenaline junkies will never understand us. "You can jump off a 6 foot wall and roll? I can dive off a 800 foot bridge with a bungee cord!" While your bro might not be into that himself, the mindset is still there in society.