Question about Jim and Claire's relationship

Question

In the first Mission: Impossible movie, towards the end, Jim Phelps kills his wife, Claire. Up until then, we know that they were working together on framing Ethan. So why does he go ahead and kill her instead of shooting Ethan and getting away?

Answer 1

Well, I'd dare to say their relationship was never that strong and it certainly didn't get better from her engagement with Ethan, may that have been staged at the beginning. When she approaches Jim (or rather Ethan in the Jim costume, with the real Jim eavesdropping from behind) at the start of that scene, she pleads for him to leave Ethan alive, although that certainly was not the plan:

Claire: Ethan's right behind me. Listen Jim, is it such a good idea to kill him? Kittridge is here. We'll take the money, Ethan takes the blame. No one else has seen you alive, no one will believe him.

While she gives some pragmatic excuses to leave him alive, the deeper reason, and one that Jim might also have read between the lines, seems to be that she developed feelings for Ethan during their time on the run and does not want him killed.

It is also seen that Jim concentrates on the aspect of her seduction skills with Ethan specifically in his dialogue thereafter, which shows that he's quite a bit jealous, and also that his personal opinion of his wife might not be the best anymore, if it ever was so high:

Jim: Why the masquerade, why take the risk? Well Claire, you've asked the question and you are the answer... But he didn't know about you. In all fairness Ethan, Claire was never convinced her charms would work on you. But I was supremely confident, having tasted her goods. Thou shall not covet thy neighbors wife, Ethan.

While his jealousy primarily concentrates on Ethan, he does project that on his wife, too, even if it was actually planned that way. When she then pleads for him not to shoot Ethan, he sees that she has feelings for him, too. His existing jealousy just gets too much and he gets mad on her. Now it certainly would have been the strategically better move to shoot Ethan first, but well, the anger of a jealous husband.

Claire: Don't, don't Jim!
Jim: Don't Jim?

And it actually still stays debatable if he ever intended to take his wife with him in the first place at all, seeing what kind of character Jim Phelps is.

Answer 2

Also, remember that when Jim is talking to Ethan in London about Kittridge he’s talking about himself and talks about a marriage in trouble.

In the prologue, Claire is "dead" after having seduced the mark. This had to have put more stress post-marriage.

The feelings for Ethan at the end were the final straw. He was cutting all loyalties.