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In short: charge is not the only thing that defines a particle. Although the charge of the neutrinos is zero their spin differs.
A longer form of this answer is here. The answers go a bit more into detail on why "zero charge" isn't precisely correct either but I'm not sure if that goes too deep for what you're interested in!
https://physics.stackexchange.com/questions/338917/what-is-the-difference-between-a-neutrino-and-an-antineutrino#338924
I'm going to copy-paste the exact relevant bit here:
I knew about the chirality difference, that there are no right-handed neutrinos nor left-handed antineutrinos (or something along those lines, breaking what was thought to be a fundamental parity or symmetry), but what puzzled me was that I thought the charge difference was the one big fundamental difference between matter and antimatter, and suddenly tonight the neutrino question popped into my head. At the very least I knew that it's not a mass/negative mass type of difference.
Now as for that bit that says "opposite signs of lepton number"... I'd never even heard of this concept or characteristic, until right now.
On further thought, this is really strange.
I can visualize a negatively charged electron and a positively charged positron making contact and annihilating, how the minus and the plus cancel each other.
But what is it about neutrinos and antineutrinos that make them cancel out when they come into contact? What is it about their positive and negative characteristics that can make them go "poof!" in a burst of photons?
A visualization you could try (this obviously isn’t going to match the physical reality necessarily) is what would happen if you had two vortex phenomena (like tornadoes or whirlpools) spinning in opposite directions and they collided?
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!
I found that this is one of the few areas where aphantasia is a strong advantage :D
I can't help you finding better metaphors beside "it's like charge but different" as I have "accepted" the whole quantum topic as math that for some random reason can be used to make predictions which accidently correlate to our reality...