I think I have another argument against infinite (eternal) time.
Suppose that we have a particular object that is to move a certain distance, say 6 m. Let us begin with the idea that it takes the object 1 s to move these 6 m. That would mean that its speed is 6 m/s. Let us suppose next that it takes the object 2 s to move these 6 m; the speed is then 3 m/s. Again, let us suppose that the object moves the total distance in 3 s; the speed would then be 2 m/s. The point is that as the total time required to move a particular distance increases, the speed decreases. The total time will increase, but the speed will never actually reach 0, it will only approach it, unless you use an idealistic quantity such as infinity, which is the largest quantity in math. When the object moves 6 m in infinite time the speed would be theoretically 0 m/s. Without speed there would be no movement.