Can someone explain minion threat to me? And how I always seem to have it but the other guy attacking me doesn't?

The wiki site does a fairly good job of capturing minion behavior: http://leagueoflegends.wikia.com/wiki/Minion The best way to think about minion behavior is to remember that it is literally just an algorithm running and determining the biggest threat in the area.

To better tailor an answer to your situation, what kind of champions are you talking about? Are you melee v melee and attacking the champion while he's close to his minions (farther down lane then your minions)? With a little context, the community might be better able to explain what is happening.