Because the photon goes through both slits simultaneously. It can’t do that if it’s a particle.
You can put enough filters between the source and slits that only one photon at a time is going through. And you *still* get an interference pattern. That’s only possible if the photon is interfering with itself. And *that’s* only possible if it’s interacting with both slits at once, which a particle can’t do.
If you stick a detector on one of the slits so you *know* which slit it went through (essentially you force it to exhibit particle-like behavior) the interference pattern disappears.
Edit:typo
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