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You need to take into account that instead of not voting, you could have voted for the other candidate.
Simple example:
7 voters, 2 candidates, A and B. 3 will vote for A no matter what, 4 oppose A. If 1 voter doesn’t vote, there will be a tie of 3-3. If 2 don’t vote, A will win 3-2. If everyone votes, B will win 4-3.
Exactly, voting for someone is helping them get into office. Therefore, voting for candidate C is helping Candidate C. It does not help Candidate A or B. Similarly, voting for candidate B does not help candidate C or A.
In your first example with a tie, 3 voters chose to help candidate A, 3 voters to help candidate B. 1 person chose to help no one by not voting. That 1 person did not help A or B. Trying to argue otherwise is nonsense. It's like saying by not downvoting a post with a misleading headline I am supporting it.
I would agree that not voting does usually hurt the democratic party, but that doesn't mean it is always the case.
Ok, I didn’t take third party voting into account, the example only works if the options are A, B or not voting. But if there was a third option with any chances of winning, things would look different anyway.
The case with the tie is included for the sake of completeness but it’s unlikely to happen, especially if there is more than one person choosing not to vote.
"But if there was a third option with any chances of winning, things would look different anyway."
Aye, there's the rub.