Basically, because our best theory of gravity (general relativity) is that gravity is really distortions in space-time. So if gravity is quantized, space-time is quantized.
But that causes quantum mechanics to fall apart; quantum mechanics is quantum phenomenon happening with particles & fields on top of *non* quantized space-time.
So we *can* quantize gravity, but then we kill our other best theory (quantum mechanics), which isn’t much of a victory.
We need to figure out solutions for both gravity and quantum mechanics that don’t break each other. This has, so far, proved…elusive.
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