It’s that there isn’t any such thing as “red-antired,” “green-antigreen” or “blue-antiblue” as you’re thinking, but rather that there are two gluons that can interact with (and be exchanged with) any color-charged particle regardless of the quark’s actual color. To picture the completely symmetric colorless combination is to picture the one gluon that cannot exist.
Linear algebra doesn’t help much either; you really need advanced group theory to learn about the properties of the SU(3) group.
And then, when you learn that, when someone asks you, “why are there only 8 gluons,” you’ll say, because 3^2 – 1 = 8. There are some things that I just do not know how to explain simply, and this is one of them.
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