In part because the “popular” meaning is derived from an attempt to secure humans a “special” place somehow distinct from other animals. Prior to widespread acceptance of evolution, no one would have considered it important to distinguish monkeys from apes, but once humans became apes we couldn’t be dirty monkeys! Sure we “descended” from them distantly, but we were different and special. So the ape/monkey distinction had to be emphasized, especially in response to the taunts of anti-evolutionists.
And, of course, the ape lineages are all twisted around to ensure that we don’t share a genus with other dirty apes.
Of course, we’re all fish too, by that measure…