Can you explain this logic a bit more because it genuinely confuses me, but I hear it articulated so often that I feel I must be missing something. I find it helpful to walk through the logic:
For example, it is frequently framed that there are only two (real) candidates, not voting or voting for a third party is the same thing as voting for <person I don't like>. The <person I don't like> is always Trump if you're talking to someone more on the left, and is Hilary/Biden/Kamala if talking to someone on the right, but the logic is the same (a contradiction should already be starting to be apparent). Both people are using the same logic to make the same claim, but they obviously can't both be correct.
It seems to me that the choice isn't actually binary. At least, if you insist that it is, then you must also conclude that a person actually gets two votes, because consider the following scenario:
Imagine that both major candidates (Candidate A and Candidate B) each deadlock and get 10 votes per, and a third party Candidate C gets 1 vote. I also have a vote, with the following possible outcomes:
1. I vote for Candidate A. This brings the total to A: 11, B: 10, C: 1
2. I vote for Candidate B. This brings the total to A: 10, B: 11, C: 1
If it were a binary, there wouldn't be any more possible outcomes. Yet,
3. I vote for Candidate C. This brings the total to A: 10, B: 10, C: 2
4. I abstain from voting. This brings the total to A: 10, B: 10, C: 1
All four of those outcomes are mathematically different, which doesn't seem possible if it's actually just a binary choice. If the outcome is different when I vote for Candidate B vs voting for Candidate C or not voting at all, then it seems self-evident that they are not the same thing. If I vote for A or B then they win, but if I vote C or not at all then there's a deadlock and a runoff. Clearly those are not the same thing.