There is a feline version of HIV, called "Feline immunodeficiency virus", so your premise is wrong.  There are also bovine and simian (monkey) immunodeficiency viruses (BiV and SIV respectively), and similar though somewhat more distant relatives infect horses and sheep and goats (Equine Infectious Anemia virus and Maedi/Visna, respectively).  

The question becomes, Why are dogs the odd ones out, and the answer is, It's just one of those things.  Not every single virus family happens to infect every single species (which is probably a good thing), and the reasons why not presumably involve ecology, evolutionary history, and a large amount of chance.

Edit to show a set of viruses related to HIV.  This is a phylogenetic tree, meaning that the distance between two viruses represents relative evolutionary distance.
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Animals are affected to aids....they are just like human do...