We do a lot of different things but we typically don't make an organized effort to eradicate them unless they are actively doing us harm.
There is also a massive difference between how we treat animals based on their similarity, sentimentality and utility to us; we are unconcerned with accidentally stepping on an ant but most people would be very upset and ashamed if they accidentally hit a dog with their car.
So, your statement is not as ironclad as you seem to think it is and you should put more thought into it and perhaps re-examine your reasoning.