One thing that has surprised me in this thread is that no one seems to be talking about what seems to me the theme of the season–hell, the entire show: the group’s moral degeneration. I think Beth was chosen to die to highlight how the group has fallen.
Consider a few things. First, a deliberate parallel was drawn between Rick and Gareth (and by extension, Team Grimes and the Termites) in the very first season. It’s not an accident that they named that cop Bob. Rick’s posture and verbage as he was preparing to murder a helpless, crippled opponent were a disturbing echo of Gareth’s barbecue monologue. Rick’s version was less stupid and less rationalizing than Gareth’s, of course, but nonetheless it made very clear that a formerly-good man had become quite brutal, if not yet entirely corrupt.
Now Beth. I loved the character and Emily Kinney’s portrayal of her, but she hasn’t been the little bitty pretty one, the innocent singer and babysitter, in quite some time. Her size and cuteness hide how cold and detached and brutal she too had grown. She didn’t lose her temper at Dawn; she was planning to at least wound and if possible murder her for some time, sheerly out of a desire for revenge. Recall that the scissors she used were the same ones she had hidden on her person in the episode focusing on her–the scissors she was prevented from using by Carol’s arrival. Said scissors were too small to be effective anti-zombie weapons, but might suffice to kill a human, and she hid them in her cast when she knew that at the very least the two most badass men in Georgia were coming to get her. It was pretty clear to me that her embrace of Noah was a feint. She needed an excuse to get within arm’s reach of Dawn–who, though certainly duplicitous and venal, had revealed herself as not entirely evil in this episode. But she had harmed Beth, and Beth wanted revenge, even when reason should have told her that she was endangering her own friends in seeking it.
Which brings me to Gareth. I think I commented on the stupidity of the Termites’ plan in their last appearance–how their desire for revenge had so unbalanced them that they were willingly and needlessly starting a fight with a clearly-superior force. The whole encounter was an unmitigated disaster for them, just as Beth’s assault on Dawn was an unmitigated disaster for her.
Team Grimes was/is on the way to becoming the Termites. Beth was furthest along that road, and it cost her her life; but Rick is on the same highway and hitting all the same motels.  Now, they won’t become cannibals like the the Termites, because they have civilizing influences–primarily Tyreese and Judith, and the several bonds in the sub-groups. But as Human Action pointed out two or three seasons back, they’ve become dangerously tribal and ruthless.
ETA: Nothing in the above should be interpreted to mean that Father Gabriel should not have his hands and feet chopped off.