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Imagine if you dug a hole in the ground. In order to dig the hole deeper, the soil needs to be piled up somewhere else. Then, imagine if you decided to move the dirt pile on top of the hole - what would happen? The soil would fill the hole, and you're left with nothing. We are simply returning to the original state of things.
That's the core idea of particles and antiparticles. At the very crux of things, there is only energy. But sometimes, the energy is able to disturb a quantum field and that produces a particle and antiparticle. The fact that the charge of the particle/antiparticle pair is opposite is not the central property of this pair. Rather, the central property that distinguishes them is more fundamental. They are fundamental opposites, and as a consequence of that fact, then they have opposite charges. They also have opposite spins for the same reason. To put it more briefly, they aren't opposite because they have different charges. They have different charges because they are opposite.
When a particle and antiparticle touch, because they are fundamentally opposites, they will cancel each other out, and the energy that went into creating them gets released.
In the way you describe it, electromagnetic charge is kinda easy to visualize. But when we get into Weak Force interactions, that's when these other, much more abstract features come into play.
For example, when you say "Spin" you don't mean regular ol' Angular Momentum, I'm guessing, but other weird types like Isospin or I-don't-know-what.
This is all fascinating stuff, truly. And way beyond my pay grade, lol!