"He cannot see those cats."
Translation:On ty kočky nevidí.
I disagree, "cannot see" and "not be able to see" feels far more like sinonyms than "cannot see" and "doesn't see". As far as I understand the sentence "He cannot see those cats" is that whoever is trying to see those cats, he is not able to see them for whatever reason. Therefore: On nemůže ty kočky vidět. just sounds right. "He doesn't see the cats" just feels as the only correct translation for "On nevidí ty kočky."
In that case just accept that "nemůže vidět" is used very rarely in Czech. Normally "cannot see" should be translated as "nevidí". Even when it is about some obstruction or other problem with ability to see.
Naši sousedi vidí do naší zahrady. - Our neghbours can see into our garden.
Přes ten strom tě nevidím. I cannot see you through the tree.
In English, the two are interchangeable when talking about senses. In Czech, when you say "On nemůže (něco) vidět.", it implies that there is some obstacle. His eyes are closed, he is in a different place, he is looking in a different direction, busy doing something else and many more, basically as if the "can" in the English sentence had the original meaning, if that's understandable.
For the above sentence, the translation "On nemůže ty kočky vidět." is perfectly fine and natural.
another example: He can see it, but does not see. - On to může vidět, ale nevidí.