This is yet another wording to try (worked for me recently) in trying to get it to click for people that IRV counts unfairly and unequally:
In RCV, if my 2nd-choice is eliminated in the first round, I don’t get that preference ever counted, even if my 1st choice gets eliminated later.
Some preferences get counted, others ignored, and that simple fact makes it far less democrat and fair. If I really care about my 2nd choice getting counted, I need to strategically put that 1st (favorite betrayal), and then we’re back to lesser-evil voting!
That should make it clear, and again, every single pathology of RCV can be derived from this fact.
A spelled out example case (click to expand)
For example (just to show the concept), say A wins over C. The 2nd-choice of most voters, B, was eliminated in the first round. Only the B-1st voters get their 2nd choice to decide between A vs C. The craziest, craziest fact (non-monotonicity) is that if C voters want to stop A, they can vote for A first!!! By switching their votes to A, that means less 1st-choice votes for C. If C drops enough, then C will be eliminated in the first round instead of B. That means the C voters are the only ones who get their 2nd choice counted. And since their 2nd choice is B, B will win. Of course, it makes more sense for the C voters to just strategically vote for B rather than vote for A. The point is: the C candidate is a spoiler. By existing, they remove enough votes from B to get B eliminated, but some B voters have A second, which makes A win. So, the C voters need to either directly help B or just otherwise sabotage C (their actual favorite) so that only the C voters get their 2nd choice counted. The mathematical fact is that one way to sabotage C is to vote for A, and that means more votes for A can make A lose! Really, this is just a bunch of nonsense around worrying about who gets their 2nd choice to count. It all happens only because RCV fails to just count everyone equally.