Humans and chimps have 98% identical DNA. Why don’t we look twice as similar as do tigers and housecats with 96% sameness?
Because we wouldn't -- it's 98.8%, while the kittehs named there are 96%, a difference of 2.8%, which isn't twice as much. The New World primates have a number of common characteristics, but their chromosome counts vary widely. Chimps/bonobos, gorillas, orangutans, and gibbons each have 24 chromosome pairs, compared with 23 chromosome pairs for (most) humans.
Humans were *believed* to have 24 chromosome pairs until *after* the discovery of the double helix structure of DNA. Some nimrod had declared the count, and no one had ever gone back and checked the work, presumably because it fit the narrative of Upchuck Darwin.
"For thirty years, nobody disputed this 'fact'. One group of scientists abandoned their experiments on human liver cells because they could only find twenty-three pairs of chromosomes in each cell. Another researcher invented a method of separating the chromosomes, but still he thought he saw twenty-four pairs. It was not until 1955, when an Indonesian named Joe-Hin Tjio travelled from Spain to Sweden to work with Albert Levan, that the truth dawned. Tjio and Levan, using better techniques, plainly saw twenty-three pairs. They even went back and counted twenty-three pairs in photographs in books where the caption stated that there were twenty-four pairs. There are none so blind as do not wish to see." (Matt Ridley, Genome: The Autobiography of a Species in 23 Chapters, p 23-24)