how come it's okay for stefan to kill vicky to save elena but when elena kills jesse to save damon?

Maybe because Stefan was a vampire for longer, so it was expected that he killed a lot of people so it almost became generally accepted. One of Elena's biggest traits was how much she cherished life and how far she was willing to go in order to preserve it, but she also loves her family and friends fiercely so I don't think it was wrong of her to step in and save Damon.

And considering how she was human before, she wouldn't have had the power to kill Jesse, but now that she's a vampire she can step in and protect them herself, so maybe it just seems overlooked because elena has only been able to kill recently (in comparison to damon and stefan for instance).

Caroline was also only really upset because she had a thing for Jesse and I don't think Elena meant to kill Jesse, but it was just a consequence of protecting Damon. Like Caroline killed those witches in order to save bonnie, so it's not like she can really judge, she was just upset because her love life is been going sour, and it was just a bad situation either way if they killed Jesse or not.

I know, its ridiculous. Its because people are just fishing for ways to hate Elena now and they don't like how she's not innocent anymore. Its called character development.

it was okay for Elena to save Damon from Jesse. Elena protects those that she loves, it wasn't intensional either one. So it was out of love mostly.

You see, Stefan has a halo. He can do absolutely nothing wrong because he's an angel, a gift from the gods. So what if he's a ripper? To paraphrase our goddess Caroline, at least he's not a manwhore.

And speaking of dear Caroline, they radiate goodness and sunshine together, don't they? It just warms my heart. Not like Elena (ugh) and Damon (double ugh). Those mere mortals think they're all that.

(Note: I don't hate Caroline or Stefan. I just wish the show would acknowledge their faults)