Remplace every time you say "animal" with "Jew", then try not to be a nazi.
This only works if you consider animals to be equal to humans, which they obviously aren't. And even if you do consider animals equals with humans, there are still several disanalogies to be offered here.
Humans killing animals are rarely done simply to rid the world of these inferior animals. Rather quite the contrary, they are done for one of three reasons:
1. To make food for humans to eat
2. To make a trophy out of and display your wicked skills at hunting
3. To get enjoyment out of killing the animal, such as I used to do with ants
None of these are actually comparable with the holocaust.
The nazis were obviously not eating jews, and this is a completely ridiculous and unsupportable claim.
For the longest time, the scale of the holocaust was kept a secret, so obviously another no on this one.
It's hard to argue that the nazi leadership got enjoyment out of killing jews since they didn't do it personally. While your run of the mill ss agent of whatever may be some phsycho bastard who did enjoy it, I doubt a majority of the 8 million nazis actually enjoyed the experience they got from personally killing jews. In fact, some, like Schindler, even tried to help Jews.
And this is all considering animals equal with humans, which again they obviously aren't. In fact, even though there aren't any people killing animals simply because they are inferior, I would argue that this is a perfectly fine thing to do. Why shouldn't you be able to kill members of races that are inferior to you simply on principle?
And just for reference no, I don't believe that jews are inferior to germans, I'm not condoning nazism here.