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It's not addition, it's division . If you divide a finite pool of votes among more candidates, the effect is that candidates similar to each other will draw from the same pool of voters, while not drawing votes from the candidate most-ideologically opposed to them. Imagine, if you will, the scenario with a green and blue candidates B and C, where a third (let's call him "A", and place him close to the greens) gets in to the race.
A is third-party, center-green
B is green
C is blue
In this scenario, there are two candidates dividing the pool of green/center-voters between them. A and B probably aren't appealing to any of C's supporters. Let's say that A and B got 25% and 35% respectively, you've got a green-blue split of 60-40 that awards the blue candidate victory because it got the remaining 40% and A and B split a green-majority's votes enough to lose. A entering this race divided (or diluted) the greens' available votes.
Because splitting up a majority of votes can hand victory to an undivided minority party, there is very much an incentive for voters that don't want their side to lose to coordinate voting to vote on the one that "can win". This involves betting on how other voters will vote, in order to avoid splitting their majority. That in turn transforms voting from an exercise in selecting your preference into an exercise in voting where you think other voters on your side of the spectrum will vote.
A ranked-choice voting system (which allows the voter to signal their choices in ranked order) does not require them to vote in the way they imagine most of their ideological allies will vote- it allows them to send their preferences as discrete signals instead.
If you don't understand this, you don't understand it, and you would do well not to finger-wag about basic math