Apathetic rhymes with:
empathetic, parasympathetic, pathetic, sympathetic, unsympathetic, empathetic, parasympathetic, pathetic, sympathetic, unsympathetic
Apathetic sounds like:
abadaka, abates, abbott's, abides, abitz, about's, abts, abuts, apatites, aphids, apodaca, apotheosis, appetites, aptitudes, avoids, avtex, avtex's