Here's a perspective from a brand new quilter.
I do it because I believe it's a dying art. There aren't many people that I know in real life who quilt. The women in my quilter's guild are all easily 20+ years older than I am (I'm in my early 30s). I started because I wanted a baby clothes quilt made from my daughter's infant clothes, but didn't find anyone that I really trusted (this was before I found my guild). So I decided to learn how to do it myself...and I found that I really, really enjoy doing it. And the best part? My 3 year old LOVES to help me quilt. She will hand me pins, or put pins in the "tomato". She loves going to the fabric store with me and picking out fabric. So for me, what started as me trying to do something I couldn't find anyone else to do turned into something that I LOVE to do...and something that my daughter LOVES to do with me. I'm hoping that her love of quilting continues as she gets older.
BTW...I still haven't gotten up the courage to cut up her clothes...