Do you find it difficult to believe that mice and rats share a common ancestor?
No, because mice and rats are both in the family. However, mice, rats, moles do not have a common ancestor as a mountain lion, cougar, panther, or short-hair tabby.
If you tear apart 3 cars down to base mechanical structures, a Ford F150, a Chevy 1500, and a Dodge Ram 1500, they’ll look the same; sure. But they are completely different. They have the same parts, but they are put together a little different.
We’re the ‘same’ as a lot of animals on this planet, because of all the planets that exist, this one supports life - we know that for a fact. The raw materials for life are going to be similar, just like the engines, transmission, etc. for the trucks. But they’re going to be different.
Just because you look at a mouse and a rat and see that they are “both in the family” but fail to recognize that humans and chimps are “both in the same family” doesn't make one axiomatic and the other an impossibility.
Zoologists classify humans as a primate, because we are. Among the primates, the two that are closest related are humans and chimps.
I suppose you have no problem looking at a chimp and a gorilla and seeing that they are “both in the family”. But by what criteria do you include two species that are further apart in DNA as part of the same family, but fail to include the two members that are the most similar in DNA?