Well parents can have a huge impact, especially since the girl in question is a bit younger than yourself.
Its an honest concern. If I had a teenage daughter, I wouldn't want her to date anyone up to a year older, but honestly, it does happen a lot.
I am not a parent, so I don't know how parenting works, I'd be worthless to try and explain anything with that.
From your parents standpoint, do you think they would take your dating a younger girl badly? If so, why?