If humans became extinct of course it would be better for the earth. But let me ask you this: Who, if not humans will be able to appreciate or even comprehend the improvement of the earth? Humans are the most self aware and intelligent beings on the planet. We are the only ones who know it will come to an end (be it ten years from now or five billion,) and the only ones who know it could be better. If we just up and vanished, no animals would be likely to even notice.
Animals are practically robots, acting entirely on instinct. Humans have hopes, dreams, and can understand the world around them much better than any other animal. Why destroy the most intelligent being to improve the earth, when there won't even be any intelligent beings left to understand it was improved? All the animals would be none the wiser either way, except for some confusion when they find the tree their nest was in was gone, and then a brief struggle for life before death.
It's better to just try and better the world without destroying ourselves. It can be done, it's just not being done.