Life would be boring without suffering and hence why some prefer to offload this on to others so as to make these other lives more interesting.
But apart from this flippant comment, even if true to some extent, suffering seems to ride along with existence, and even if we can ignore physical pain - examples to show this - and as to much else simply being down to our responses to any suffering, the very nature of life (as pointed out by others) is towards survival, and as to such, conflict inevitably arises because there are such a variety of lifeforms.
As top predator, why would we think that our suffering means more than any others? Apart from any belief that we are in some ways so superior to all else. And where would this notion come from - oh gee, so many of the religions, and where such beliefs might just have come about to justify our superior stance. The superiority is not a view I have come to believe, and as to why I am less inclined towards having favourable views concerning religions - as seemingly being so anthropomorphically biased (Gods as projections of humanity).
To me, the elimination of suffering, if even possible, would likely lead to a very sterile world, the destruction of so many other lifeforms, the emasculation of humanity, and probably, the pointlessness of even existing. And this coming from a very non-religious viewpoint.