This conversation is going in circles. It has been stated many times in this very thread that Jean did not necessarily love Logan. And as a matter of fact, it is quite irrelevant. In fact, I think it's not really important if even Logan loved Jean. Here's how I see things:
1. Phoenix killed Scott not because Jean didn't love him. That was the first emergence of Phoenix. Because of that and because not even Jean expected it, she totally lost control of her mental state and her powers as well. I think that's what knocked Jean out and that's why initially she didn't remember any of it.
2. In the climax Logan stated that he was the only one who could stop her. He would try to help Jean resurface but he expected to take some damage in that chaos. Maybe others could have reached her too, but they'd probably not survive. Plus, due to the fact that Logan was more to the liking of the Phoenix (and maybe due to whatever feelings Jean had for him, not necessarily love, mind you) she would be more lenient towards him.
3. As I already said, I'm not really sure if it matters if Logan loved Jean or not. Sure it played a part, but I think Logan would try to do the same if it was Storm or somebody else in Jean's place. He would try to make them come to their senses and somehow sort it out. I think it fits Wolverine's character, he doesn't really care about himself, but he'd do anything for those select few that are close to him. His feelings for Jean just added to his motivation.
4. Phoenix certainly wasn't trying to kill him. She simply toyed with him. We'd seen earlier what she could do, she had thrown Logan across the room, she'd demolecuralized people in a split-second and wrecked entire buildings, she was a powerful enough telepath to challenge (and maybe defeat) the professor. The entire island was being destroyed but she spared Wolverine, because the animal in him was fascinating to her and she wanted to test his behavior. Maybe Jean held her back a little too, it doesn't really matter. So, with every step he took, she tested his limits, wondering how much he could take and for what reason. Of course, when he reached her, she wasn't even in the slightest worried about him. She just did not understand his motivation. Hence "You would die for them?", as she mistakenly thought. His answer, unexpectedly, brought Jean to the surface. And from here on, it's all Jean. Here's the redemption peolpe expected from her. With some help, she managed to subdue Phoenix and she fully realized what she'd done and what a danger she would be to everyone. And she knew there was only one way to redeem herself and ensure everyone's safety. So she kills herself. Wolverine doesn't kill her, she kills herself. He's just the tool. He asks him to do it, and she holds the Phoenix back long enough for her to die. If the Phoenix was in control, maybe Logan's claws would not be enough to kill her. But at that moment she's holding everything back, she's a normal person with no powers. So she dies, having finally found peace as the menace of Dark Phoenix is now gone.
That's my take and I find it to fit in the movies' context. You don't have to accept it, but at least try to think of it like this and see if it does it for you. I'd like people to be able to enjoy this film and see past their initial expectations and beyond the inevitable comparisons to the comics. I'd also like to add I'm primarily a Spidey fan and have no real preference over Scott or Logan. I just find much of the criticism towards this film somewhat unjustified.
Sorry for the long post.