"The earliest known examples of Mithras worship date back 4000 years to the Persian empires"
...so the old testament writings do not predate the Mithras mysteries quite so easily.
It was stated in the rebuttal, "the Old Testament was begun around 2000 B.C. and completed around 400 B.C." That means that the Old Testament was begun around 4000 years ago, about the same time that the earliest known examples of Mithra worship was around. So, its possible that neither predates the other.
And yes, I'm sure, 'who influenced who' will certainly always be up for debate.