Short answer: particles are not waves. Rather, what we usually think of as particles (like electrons) are something different and altogether weird. So your confusion about wave-particle duality is not a sign of a lack of understanding. It is a sign of understanding that what we say about quantum theory doesn’t respect our intutions about either particles or waves.
One way that electrons show wave-like behavior is [interference patterns]
(https://en.wikipedia.org/wiki/Wave_interference). You can shoot one beam electrons at a detector, and where they hit looks somewhat random. But if you shoot *two* beams at a detector, you get a pattern. Electrons stop showing up where they used to, even though all you’ve done is shoot *more* electrons there.
Our only explanations for that involve waves. We need to fiddle a bit more with our understanding of waves to make it a *quantum* wave theory. But once we make those changes, we can describe electrons (and a bunch of other stuff) pretty well.
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