Eternal Recurrence from Anaximander

"The beginning and origin of the things that are", Anaximander says, "is the Indefinite [apeiron]. Into that from which the things that are arise, however, they pass away again, as they are obliged to do; for they give satisfaction and reparation to one another for their injustice, as is appointed according to the ordering of time".

I pulled that from R.J Hollingdale's concise Western Philosophy. It got me to thinking about Nietzsche's eternal recurrence. When I raised the idea with my philosophy professor he somewhat dismissively said that it was a mostly psychological concept to get one thinking in terms of absolute meaninglessness - which might be true, but is is really a bad theory of time? What are the arguments against it? I think my professor mentioned something mathematical about how things could recur infinitely and never hit the same old point again. But stretched infinitely, it seems like it would hit that same old point again, and again, and again(even if it's done it once, there's a pretty darn high likelihood it's gonna do it again). Infinity -- such a conundrum.

The comment from Hollingdale immediately proceeding from that is:

These sentences, the earliest surviving complete sentences of Western philosophy, contain, it has been suggested, the ethical judgment that all created things deserve the destruction which is awaiting them, and that Anaximander is thus an ethical pessimist of a kind similar to Schopenhauer.