"Leid tun" doesn't mean "to hurt feelings" but "to evoke pity" or (when you swap subject and object) "to feel sorry".
So I'd translate that line as "'cause I feel sorry for animals".
I'm not sure whether you understood the second line correctly. Is "harvest" an expression for eating very much?
"But eating meat is finally over for me"
Your translation omits the expression "(Fleisch)Genuss". I'd change it to
"But the joy of eating meat..."
"so manche" means "many a".
"For me, no more animals will be dead"
In the German line, it says "tot machen", which is something like baby-talk for "to kill". I'm not sure whether your translation reflects that.
"when they want to tell you,"
"Albeit I become jealous when someone eats steak."
"Wenn's Würstchen noch so lacht"
That literally means "no matter how much the sausage laughs".
When food "anlacht" someone, then that means that it looks delicious.
"And shit doesn't stink so much anymore"
I'd change "shit doesn't" to "my excrements don't" to make the meaning clearer.
These are the official lyrics, taken from the "die ärzte Songbook", only slightly reformatted. Also, the line "Nein" was added.