Cosmological arguments are based on the idea that something was necessary to create the universe as we know it.  There are three outstanding problems with such arguments: (1) the idea of causing the universe itself is nonsense, (2) such arguments irrationally prefer inexplicability of the supernatural over the natural, (3) the arguments are an appeal to ignorance.

Firstly, we have learned from theoretical physics that matter/energy and space/time sprang into existence several billion years ago, but to posit a cause for this is not merely unnecessary but actually irrational, since the concept of causation is dependant upon the existence of time. Nothing can have caused time, since causation itself cannot exist apart from time.

Secondly, whereas the theist demands an explanation for the existence of the universe, he does not demand such an explanation for the existence of God.  The atheist, on the other hand, is happy to take the existence of the universe as given.  It is evident that our chain of explanation must of necessity end with something inexplicable, but there is no compelling cosmological reason to believe that inexplicable something must be some sort of sentient, supernatural, personal being rather than the universe itself.

A final point against cosmological arguments is that they engage in a kind of appeal to ignorance by attributing that which cannot be explained to a supernatural power.  It is not rational to claim that a present lack of a natural explanation implies a transcendent answer.  Once upon a time we could not account for the existence of the sun and moon, so we created myths of gods traversing the heavens.  We created fertility gods, rain gods, gods of lightning, gods of death, and all manner of other myths to explain all of the mysterious forces and events which shaped our lives.  Over time, we have realized that these phenomena are all governed by natural laws.  Just as we were mistaken then to impute transcendance to that which we did not understand, so now there is no reason to credit a transcendant being with creation of the cosmos on the grounds that we fail to understand just how it happened.