It doesn’t end with “hurt you” because A) it doesn’t and B) it sounds weird. It ends with “desert you” because A) it goes with “run around” and B) it doesn’t repeat then
NEVER GONNA GIVE YOU UP, NEVER GONNA LET YOU DOWN. NEVER GONNA RUN AROUND, AND HURT YOU. NEVER GONNA MAKE YOU CRY; NEVER GONNA SAY GOODBYE. NEVER GONNA TELL YOU LIES.. AND HURT YOU!