My son Gabriel just turned 6 and I have been wanting to give him a Daisy Red Ryder BB gun (set aside for him) for a while now, Mom has been encouraging me to hold off... But the day finally came and on his 6th birthday he got it! As you can imagine, Gabriel is very interested in guns as he watches Dad shoot guns all the time.
I have been educating him on how to handle guns since he first showed some interest so he knows all the basics like; treat guns as if they are loaded at all times, never put your finger on the trigger till you are ready to shoot and never point a gun at anything you do not want to shoot.
There is no right or wrong age at which you should introduce a young person to sport shooting, it is really dependent on the child and the parent who is willing to train the child. There are many adults who should not be in possession of a gun (even an airgun) as far as I am concerned and this may be in part to little or no education from their parents!
My son will only be shooting his Red Ryder when accompanied by myself or another adult I trust to watch over his shooting. At some point Gabriel will be allowed to shoot on his own but he needs to show me he is ready and I am sorry to say, but a 6 year old is just too unpredictable even if they are very responsible for their age.
Funny enough, now my 8 year old daughter wants her own BB gun :)