They go through the same hole as the mouth in the end, though.

Yes, but they're distinct openings, which means we're not topologically equivalent to a doughnut when you take them into account. Topological equivalence implies that you can transform one object into another without changing the number of openings. Classic example is a doughnut and a coffee mug (the handle of a coffee mug is the opening). A human would be equivalent to a doughnut with two holes poked through the side into the middle.