If man has no purpose, why would animals have any?

Over the years a reoccurring statement or belief is that man and his life here on Earth has no purpose, he just is, and just happen to be here. If that were the case, then animals, which are lower than humans, would have no purpose either. That would mean if man drove any species to extinction it would not matter, nothing would happen positive or negative by erasing any animal insect, or even several species would not have any significance. If there are any consequence to such it would just be in the mind of men for whatever reason man wanted to view the extinction, be it positive or negative. Why would animals have a purpose and not man, would that not make man the ultimate parasite?