Keep in mind that people typically complain about the thing they think they can defend. Their actual gripe may be wholly unrelated to their stated issue.

Indefensible issues can include:

"I'm jealous."

"He's wicked smart and it makes me feel inadequate."

"He's hot. I would hit that, but I'm married and he's a coworker, so no. Now I need an excuse to hate on him and alienate him."

That last issue is one they should not admit to, you should not poke at, etc. But it also shouldn't be a reason to fire a guy. Reality: A lot of people cannot cope long term with platonically working with someone they find attractive and this is frequently resolved by one of the two changing jobs.