Rush framed the guy for murder. And flat out told him he'd never stop coming after him. At the very least that means Rush is going to try and undermine Young's authority, thereby putting the crew at risk. At worst, it means Rush is going to kill Young. That's either mutiny or murder, either one punishable by death in the military.
And once Rush admitted that he was never going to stop going after Young, and that he'd do whatever he wanted, he became a liability to the mission. Instead of working to get them home, Rush is working towards his own endgame, and Young had to put a stop to it.
Rush saying that he will never stop means JUST that. That he SAID he would never stop. You don't strand somebody on a deserted planet over something he SAYS. Let's not forget that Rush and Young did work together when the situation called for it.
Rush never placed anybody in danger willingly, he never killed anybody or threatened to hurt anybody. Never stole food, never held anybody at gunpoint. If anything, more crap has happened to him than he has inflicted on other people. The thing he did wrong (on the ship) was to state from the beginning that the only way they were getting home is if they know Destiny's secrets and he devoted himself to learning those secrets. Fact is that he is more interested in learning those secrets for himself than the rest of the people, but that doesn't infer his initial statements. They DO need to know more about Destiny to get home, and he is the gateway to that. But Young isn't comfortable 1. depending on Rush and 2. letting somebody like Rush get the knowledge he desires. And that's why I think he left him on that planet. Not because it is in the INTEREST of the group.
And again, maybe we're reading too much into it. Young might have had no intention of leaving Rush behind. Just give him a beat down to remind him who the alpha dog was, and to stop ****ing around. But Rush had to keep pushing those buttons, and Young knocked his ass out. At which point, both of them were screwed because Young didn't have the time to carry him back to the gate. It was either leave Rush behind, or they both get stranded.
Correct me if I'm wrong, didn't Young drags Scott's ass out of that ice crevice? By himself? And he had to carry both Scott and his 100 pound suit. And isn't Scott a bigger guy than puny Rush? You actually expect me to believe he couldn't have carried Rush out of there? Heck, maybe if he slapped him around a bit maybe he could've waked him up!