That's not what happened at all.
- Qhorin tells Jon that one crow in Mances army is worth how ever many outside.
- Jon tells Qhorin that they'll never trust him.
- Qhorin tells Jon that they will if he does what needs to be done and then pushes him down screaming that he's a traitor.
- Qhorin attacks Jon all the while calling him a turn cloak/traitor/etc.
- Jon does as Qhorin instructed. He did what needed to be done.
Just because Qhorin didn't say "Kill me Jon" doesn't mean it wasn't heavily imply that he wanted Jon to do something extreme in order to get in with the wildlings. It was obvious that Jon knew what Qhorin was doing.
Problem is they whispered so quietly and subtly that none of the wildlings could hear. Unfortunately neither could the audience.