There’s your problem. Not every male passes on his Y chromosome. That only happens if he has sons. All the mutations that happen in males who have no sons are lost. Further, given most reasonable assumptions, every strictly male lineage except one will eventually be eliminated because all it’s various branchings will end in daughters (or extinction, which is the same thing as far as Y chromosomes are concerned). This is true whether the population is expanding, contracting, or stable.
Then again, barring selection, that one remaining lineage will have experienced a number of substitutions per generation equal to the mutation rate per generation unless selection has been operating. And if there’s no selection, population size is irrelevant.