There’s not much to debate or understand. Anyone can look at a primate suffering and see the wrongness there. People need years of education and training to the contrary in order to reach the opposite conclusion.
I find it illuminating that you opened up with “oh gee, what purity test” and ended with “if you eat meat you have no standing to care about animal rights”.
Instead of convoluting the discussion, why not come right out and say what you want to clearly and plainly?