Many cases for the existence of God make arguments for a First Cause who must be the ground of the existence of the universe. Sometimes, part of the argument here involves pointing out that there is a logical absurdity in supposing that the past is infinite. If the past is infinite, an infinite amount of time has already occurred as of now in the history of the universe. But it is impossible to traverse an infinite, and so the past cannot be infinite. (I won't go into more detail on this point right now. For more on this, see the case for the existence of God in chapter three of my book, Why Christianity is True.)
One of the responses that is sometimes made to this argument is that perhaps time is circular rather than linear. That is, instead of conceiving of time as a line with the present as a point along the line, the past as the part of the line in front of the present point, and the future as the part of the line after the present point, why not conceive of time as a circle, where you have a present point but if you go far enough ahead on the line from the present point you eventually come around again to that same point? In this way, we can say that the timeline of history never had a beginning, thus avoiding the First Cause, without making the past infinitely long, thus avoiding the absurdity of an infinite past.
There are a number of problems with this argument, but what I want to focus on right now is the logical absurdity of the concept of circular time. First of all, let's distinguish circular time from cyclical time. Cyclical time, as I am defining it here, would be a linear timeline on which events repeat themselves. That is, the same things happen over and over again. While I don't think that history actually happens that way (at least not overall), there is nothing immediately logically absurd about such an idea. Circular time, on the other hand, is the actual changing of the time-line into a time-circle, as I described above. Here's one way of getting at this distinction: Take a particular historical event, like my birth. According to a cyclical time idea, where everything repeats itself again and again, we would say that I was born in the past and I will be born again in the future. According to a circular time idea, on the other hand, we would say that I was born in the past and that I will be born for the first time in the future. That is, in circular time, things don't happen over and over again (which is a linear concept); rather, they happen only once, but the past and the future are ultimately the same thing so that every single event is both past and future.
The logical problem with this idea is evident in what has already been said. The circular time idea makes the past and the future the same thing. But it is self-evident that they are not. They are distinct by definition. The past is "stuff that has already happened," while the future is "stuff that hasn't happened yet but will happen later." They are fundamentally conceptually distinct concepts. Therefore, any attempt to equate them results in the logical absurdity of saying that two things that are actually different are not actually different. With regard to my birth event, the circular time theory ends up saying both that "I have been born already" and "I have not been born already" (for the latter proposition is necessarily implied in saying that "I will be born for the first time in the future"). Thus, the circular time idea involves unavoidable logical contradiction and therefore absurdity, and thus cannot be true. (For more on why logical contradictions are absurd and cannot be true, see here.) The concept of time, with its necessary distinction between past and future, is essentially and unavoidably linear.