The best explanation I've seen for the notoriously difficult-to-understand Isha Kushite story goes something like this:
Who is the Isha Kushite?
Tzipora, wife of Moshe (or alternatively she is a second wife, an actual Kushite)
Why is she called an Isha Kushite?
Its a term of disparagement. (or alternatively she is a second wife, an actual Kushite)
Why is Miriam upset?
Because Moshe elected to STAY married to her after becoming a top-tier-prophet. This fits the plain meaning of the verse. ("Miriam and Aaron began to talk against Moses because of his Kushitewife, for he had married a Kushite") Miriam thinks it unbecoming for a big guy like Moshe to remain married to lowly Tzipora. After he rose in stature, he should have upgraded his wife.
Clue #1: Miriam says "Has the Lord spoken only through Moses?” they asked. “Hasn’t he also spoken through us?” The point here is that she believes Moshe is degrading the institution of prophecy. He's not the only prophet in the world. The Lord has also spoken through us, and all of us prophets look bad because Moshe persists in staying married to Tzipora. The honor of the institution must be protected.
Clue #2: This story comes after the Eldad and Medad story, which is also about someone (Joshua) seeking to defend the honor of the prophets. He says, "“Moses, my lord, stop them!” In Joshua's view, Eldad and Medad have no right to prophecize because they have not been properly elected; their unsanctioned prophecy undermines the entire institution. This same concern for the honor of prophets is what animates Miriam in the adjoining story.
Consider this possible historical analog
Source: Bar Ilan Parsha Pages.
- Talking Torah with the Baby Bears In which I discuss Miriam's sin with two people who came to the text with no pre-existing opinions about it, ie, my kids
- The view of Josephus
- More on Moses and his black wife In which I provide some classic, and not so classic commentary on the verses in question
- Ibn Caspi politely but strenuously refutes Rashi regarding the Cushite Woman