"Why do you hate him?"
Translation:Proč ho nenávidíš?
HO is an obligatory enclitic word, which makes it entirely unacceptable in the place you put it. That, incidentally, would be where you would put the JEHO that is being asked about by Paul378887. I suggest reading the Tips & Notes for the Pronouns skill.
Why does "mne" come last in the construction "Kdo miluje mne" (who loves me), but "ho" comes second here?
You can say "Kdo mne miluje" (it actually sounds little more naturally) as well as you can say "Proč nenávidíš jeho?
“Proč jeho nenávidíš” was not accepted. Why? It’s the same word order as the one given here.
Yes, it is the same word order, but the wrong word. JEHO is not 100% interchangeable with HO when it comes to placement in the sentence.
Placing the regular (long) form "jeho" in the second position (where "ho" would be perfectly fine) makes it clear that we are specifically interested in this "him", and that level of specific interest would mean that the reference to the "him" belongs to the right of "nenávidíš", not left.
This is certainly not easy to learn, but in the interest of not letting our users sound like goofs, we have to keep rejecting it.
I suggest reading the Tips & Notes for the Pronouns skill.