A Thought on Parshat Balak

At the end of the parsha is the story of Zimri, Kozbi (not to be confused with Bill). Rashi describes the situation as follows (paraphrased): Zimri was... doing the deed with Kozbi... right in front of the Ohel Mo'ed, and asked Moshe, "Is this allowed, because if you say no, then who gave you permission to marry your wife? (She was a Midianite.)

In other words, this wasn't so much an act of inappropriate sexual congress (which it was as well), as an act of sedition against Moshe. It was an attempt to bring Moshe down a peg. A "What makes YOU so high-and-mighty?"

Now I find this to be curious, because according to Rashi in the story of Korach's rebellion, there was a similar attack. Rashi there says that Korach also attacked Moshe "intellectually". I'm not going to go into that attack - too complicated. (In fact, my personal thought has always been that his attack there was a bit silly, but be that as it may...)

So here's my question, and I don't yet have an adequate answer for it: Korach had a motive. He felt that Moshe was a nepotist, dealing out choice positions to his own family-line, because he could. Korach, who was Moshe's first-cousin, felt that he had just as much a claim as anyone else to positions of power and honor, and that he had seniority to boot. So right or wrong, Korach had a motive.

But what was Zimri's motive?