Gymnastics isn't bad at all. It sounds like you're a good coach, and it's no wonder that you're interested in parkour. I'm sure that all of your students, comrades, and other teachers have the same set of value goals and dicipline as you. I'm serious.
HOWEVER a lot of people end up getting competitive even if they started out just to learn the skills. I remember when I took gymnastics.. I got very competitive, very quickly, because my coach put a lot of pressure on me to win. She always told me "I raise my students to be winners, not losers. If you lose, then perhaps you should return right back to where you started."
She sort of scared me. I can remember a lot of other girls crying if they lost because they were afraid that my coach was going to yell at them. Thus, I quit.
Sorry, personal rant. Gymnastics is great, martial arts is great... just be sure to investigate everything throughly first. Lets not forget there is competition on martial arts, as well guys. 
Yeah, sorry if it sounded like I was attacking Mathew on his opinion lol. Yeah, today I asked my friend/co-worker, about gymnastics being competitive, and he says, when your real young and you join gymnastics, they first, try to make it seem like its all fun but once you start getting good, they try to make it super serious, and competitive. He's been working at that gym for 7 years, so he basically knows how everything works.
And thanks snow, I kinda got defensive there in my first post, because me being a coach and all, iit made it seem that he was attacking me on how I make gymnastics too competitive and serious for the kids. I know that he wasn't just pointing me out.
But, I'm known as the nice, fun coach, because I try to make it as more fun and less competitive as I can. I just teach them what they want to learn and thats about it. Lol, now look at me, going on and on about my personal life, I'm gonna stop typing now...
ALSO, on a side note, I'm trying to start teaching a Parkour Class at my gym, so hopefully that works out well.