I'll go against the grain here.
I'd rather my child learned boxing.
Yes, boxing is violent. But it's also a real skill that may conceivably protect them in real life, someday. But that's kind of a by-the-by.
The main reason is that boxing does not separate a person from the violence. It's in their face (literally). They know how being hit feels, they know the damage it does, they don't take it lightly. They are very much a part of what is happening, and not shielded from the outcomes.
Additionally, due to the physical exertion, I imagine it could help a person work off aggression.
Guns, and anything that associates with them, leave me cold. Guns allow a person to kill other people (or animals) en masse, with almost no personal involvement or physiological feedback. They separate the shooter from the extreme violence and force of the act they are committing, because they themselves do not have to come close to, or feel the struggle of, the person they are killing.
Sure, target shooting is shooting at a target, not a person. But guns were not invented for shooting at targets. So while the hobby is kind of 'once removed', it's still associated, for me. And it's not a skill they are likely to use in real life - or if they are - that's not a good thing.
Sevenyears summarised how I feel about guns
No child ever accidentally beat themselves to death after stumbling on a parents' improperly stored boxing glove. Nobody ever walked into a movie theatre and boxed 16 people to death. I know there are ways around both of the above, but I simply wouldn't be a party to an activity where a gun is a recreational item despite not seeing an actual connection between that specific activity and violence.
Skill-wise, I feel that boxing is much more of a skill. It involves psychology and anticipating the other person's movements and interpreting their body language and understanding the human body and where it is vulnerable. It involves a moving target and defense. I think this probably generalises to a number of sports played against opponents whether individual or as part of a team. I think it also generalises to personal safety.
Shooting is learning to operate a specific piece of equipment very accurately. I think it generalises to... I dunno, shooting other stuff I guess.
In reality, I hope my child will do martial arts or something more defense based than attack based like boxing. I'd rather they picked up the useful skills from there without actually having to hit another person, or get hit.
But if they wanted to do shooting, I'd let them, but I wouldn't be happy about it. I hate guns.
I don't think it's hypocritical to box and be against guns. Mass murders have never been carried out by boxing.