Fair enough.
First, your logic is pretty flawed in my opinion. You are presenting two possibilities, one being widely accepted as less severe than the other (tagging vs mass shooting; property damage vs murder), implying that if he doesn't do the first, then he will do the second. Of course I would rather a kid tag a building than shoot up a school, but it's pretty asinine to even imply that those are the only two possibilities, especially considering that's such a massive leap in severity.
I'll give another analogous example that, albeit more extreme, follows the same logic that you presented: "Would you rather a kid with mental problems rape your mother/wife/girlfriend or kill her?"
I'd wager the vast majority of people, and probably you, would choose rape, as awful as that is. But, this "kid with mental problems" was sexually abused growing up, so we should treat them as a victim and not an aggressor? I am certainly not "obsessed with punishing criminals", but I am never going to go along with this.
Second, even with your reply to my comment, you are heavily implying that graffiti should be somewhat acceptable in the case of a rough upbringing, and then pretty much stating that if I am unwilling to help the troubled youth of the world, that it's somehow my fault for having my property damaged:
Unless you're willing to help him and change his ways, he's gonna stick with the outlet he knows, graffiti or whatever.
Third, the male in this video is obviously not a child, or even a "kid" as stated above. I mean he has gauged ears, a mustache, and a goatee - not a kid. Obviously old enough to know better, regardless of his upbringing.
Fourth:
not everyone was raised in a perfect home, with perfect morals.
No such thing. Plenty of people who grew up in very typical families, with supportive parents, and every opportunity in the world to succeed end up doing the exact opposite. And there are plenty of people who did the opposite: pulled themselves up out of a troubled childhood and made something better of themselves. It's called individual responsibility. Again, if this was a video of a 10 year old kid tagging a building, we'd be having a different conversation, but that clearly was not the case. The guy even admits guilt in his panicked responses to the property owner.