I mentor for many reasons:
My first experience with FIRST was in college when I was on a semester engineering co-op job. My work mentor was also a mentor for FIRST team 180 S.P.A.M. and invited me out to their shop to check it out. I thought it was pretty cool, and I actually learned pretty much everything I know about using a mill from their retired machinist mentor. This alone has been very beneficial in my engineering profession. Even as a part time college "mentor" I learned so much being part of FIRST that I want to continue that cycle of learning with students today.
Secondly, most of our students want to go into technical fields, so they really look up to me as a professional engineer. My opinion matters much more than I first imagined to the kids. I told one of our seniors last year I was proud of her, and she still talks about it like it was a defining moment of her life. I was never cool growing up, but now I feel like a rock star.
It's a pretty awesome feeling to be a "hero" to the kids.
Little kids want to grow up to be firemen and doctors. FIRST kids want to grow up and be engineers.
Third, I really like teaching. Not in the classroom/textbook style, but explaining how things work, how to use equations, why things are the way they are. I love the feeling of seeing a student "get it" It makes me feel all warm and fuzzy inside. I try to design team exercises that illustrate engineering concepts (like optimization) and still are a bit of fun; last year our team captain came up to me afterwards and said "this was really cool" which absolutely made my day.
And last -- I get to play with robots! How is that not awesome?!?