Rabbi Noson Weisz writes for Aish.com:
Moses was the man who gave us the Torah. A blemish on his character automatically detracts from the authenticity and weight of the Torah. Lashon hora always gets out, no matter how private and secret you attempt to keep it. If Miriam’s statement would have been allowed to stand unchallenged, pretty soon the average Jew on the street would know that in the opinion of his own siblings, Moses was a ruthless rabbi who was happy to sacrifice the happiness of his wife in order to satisfy his own spiritual ambitions. Instead of the caring leader they had considered him until now, the ego-less person who never considered himself and lived totally for them, it turns out that he is a self-centered spiritual social climber whose interest in them is to use them to attain greater spiritual heights.
We are extremely familiar with the phenomenon of discrediting rabbis. If you can get yourself and others to believe that rabbis are merely power-hungry manipulators, or exploiters of women, or any of the other disparaging remarks made about rabbis with which we are all familiar, then you do not have to confront the truths of Judaism. Instinctively every Jewish heart knows that when it seriously confronts Torah it will melt in the heat of its holy flame. The solution is to cool one’s ardor by bashing rabbis.
Not that Miriam meant to do this. The trouble is that one never means to do anything terrible when one utters a few seemingly harmless words of lashon hora. The world is no less destroyed when the person who blows it up doesn’t mean it.