Another argument, and one everyone should reject, is that some parents at youth sporting events are known to lose control of their better judgement and do stupid things such as starting fights. Some worry about what would happen if one of these parents had possession of a gun. Frankly, fear of such an event cannot be allowed to overrule common sense and deprive law abiding citizens of their constitutional rights.
It is probably worth considering the possibility that these parents behave irresponsibly specifically because they go through life not having to worry about catching an incoming round as a result of their irresponsible behavior. It has long been known that an armed society is a polite society. Anyone that grew up in places where every pickup had a loaded rifle rack in the back window will confirm that.