It's definitely a tough question once you accept the premise that you need to justify it. If we accept that we need to and I don't believe we do here are a couple points that I think are very relevant:
1. Total dedication to anything will ruin you. It doesn't really matter what it is. Dancers ruin their feet, gymnests ruin their knees. I'm a huge chess fan, by all accounts this is an activity that is almost universally held to be good for you, but for those who engage in it at higher levels of competition it is not. A shocking percentage of the best players suffer from mental illness late in life, which is really quite unusual as those things normally present themselves before 30.
2. Football has become relatively upfront about the dangers. Parents, children, and adult players are aware of the risk.
3. The greatest exposure to possible injury comes as an adult instead of as a child. This is different from activities like dancing and gymnastics where lots of damage to the body occurs without much of a chance to consent. Certainly this doesn't make the news as much, chronic joint pain, and bad feet aren't great headlines but we are talking about lifelong consequences to very young people.
4. Football is awesome. it's fun to play, its fun to watch, and just because there's a serious cost doesn't mean its not worth it. Either way its not our decision, its a personal decision for those who choose to play. Sure it has its problems but at least we're trying. We want it to be safer, we might not succeed but when you're talking about an ethical or moral issue effort does count for something. From the league to the players to the fans to the media we would all like it to be safer, we (for the most part) don't want players getting hurt. Getting hurt is a side effect not the point.