It... really kinda' doesn't. Much of the outrage towards the mother is for her letting the kid get in the enclosure at all, more than anything else involved. More a case of human incompetence < animal, and should be punished accordingly when it gets animals in a situation they have to be killed or injured, for those ones.
All the inappropriate vitriol aside, they've got a damn good point so far as that goes. Shitty (perhaps only temporarily, who knows) parent got their kid nearly killed and an animal outright. Generally we levy some kind of penalty against junk like that. Looks like folks are going the public shaming instead of legal route, but *shrugs*
In regards to justifying the rage, I think it is. the much of the anger belong to the complete majority opinion of Human > Animal so they naturally focus on the mother's negligence. i don't think its these people who singed those petitions. with those it's like when parents who forget their baby in a car and the baby gets saved at the last second gets raged by the internet, if it doesn't get saved, the comments are more in line, but you can still find some nasty remarks even amidst the parents grief. the fact that an Endangered Animal got killed, even though it was justified (in their minds), only allow the Mob.Net to morally excuse themselves for getting enraged at the woman's negligence.
Let's run a theoretical scenario: A woman neglect to watch her kid and that kid runs straight in the path of an incoming car. the driver can't see the kid nor see the crowd signals. you got a sniper rifle, and for argument sake, shooting the driver will save the kid. will you take that shot? i think that the majority will not take the shot, for several reasons, the first reason is that shooting an innocent human being to save another is morally wrong and the second reason is that realistically, most people wont be able to take that shot at a man even if they intellectually think it's justified in this case.
We come to this discussion, like the mother shown in her comments, with an assumption that it is ok to shoot an innocent animal, at its own territory only to save a human being. that formula is wrong, in my opinion, and even though i know it is wrong, i, like many others, was raised completely indoctrinated to believe humans are superior to animals (not for religions reasons since i was raised an atheist) so i still believe it was good to shoot the animal to save that kid. if i believe so, even though i intellectually can't find a reason to justify it, imagine the frustration the enlightened ones have when trying to teach us that Animal = Human. i don't think a calm and reasonable debate could suffice here, especially considering the religious tendencies people have in America (In Which Man is God's last and best creation). i can completely understand their rage.
That the kid got in the enclosure thanks to his mother neglect, that the gorilla is an endangered specie, that there was a very good chance the gorilla wouldn't have killed the kid and that the woman shown a complete lack of care for the gorilla and just excused herself and thanked god for saving her child only means that for some people in this specific case it managed to temporarily shift to Human < Animal and perhaps could raise awareness to that underlining issue.
The sad irony here is that there is a bigger chance the woman could sue the Zoo and win rather than the Zoo sue her and win. if she sues the Zoo and wins, the court basically says, Human > Animal, even though Human is a mindless herd animal without any need for self responsibility.