For one thing, I think it's because Ennis is supposed to be the more skilled cowboy. For another, it may symbolize whose decisions prevail in their relationship. Jack misses the coyote, gets thrown by his horse, never gets Ennis to settle down with him.
I wonder a little about Ennis being the more skilled. Ennis gets thrown off his horse, too. And gets injured. When Jack gets thrown he never mentions it until days(?) later and then only says his harmonica got flattened, nothing about any hurt to himself. (though I have wondered too if the slow and careful way Jake sits down at the beginning of their 'rodeo cowboy' scene could have been his way of showing that Jack had fallen shortly before that).
Years later, Ennis tells Jenny that he only stayed on that saddle bronc for three seconds, while Jack had ridden bulls (an even more demanding and dangerous event), and, regardless of what those two customers said, he had done more than tried to ride them. Jack wouldn't have earned the two or three thousand dollars (film or story amounts) without having some success at it.
Clearly, though, Ennis is a better shot than Jack. Symbolically, what could that imply? Maybe one interpretation, least as far the coyotes are concerned, could tie back to the sign on Aguirre's trailer that trespassers will be shot, and survivors will be shot again.
The coyotes are certainly trespassers far as sheepherders are concerned, so Ennis shoots 'em, including the one that survived Jack's attempt.
Then there's Ennis' wedding, where we hear, not "dearly beloved", or (fantasy scene material - "if anyone can show cause why..."), no, we hear part of the Lord's prayer - "forgive us our trespasses as we forgive those who trespass against us."
So who's the trespasser here, according to Ennis? (Since that voice-over starts while Ennis is kneeling in the alley, I think we can safely read that concern over trespass as being at least somewhat reflective of his thoughts.)
With good reason, Ennis sees a lot of dangers in the world and tries his best to protect those he feels responsible for and loves, and also himself, from those dangers.
If the trespasser(danger) is a coyote, that's comparatively easy for Ennis to deal with. If it's something you can't shoot, though, like awful fathers, or a condemning society, Jack, who can't shoot coyotes, proves himself more versatile (pun absolutely intended from the the name of the combine Jack is driving with Bobby) at dealing with those threats that "trespass against us."
But why can't Jack shoot coyotes? Maybe to show that he can't deal with the dangers to them in a way that would make Ennis feel safe.
