Fallacy:
"I have yet to see you post one single statistic number or fact to base your [rational arguments] on!" (Lorie DeBehnke)
Response:
I won't argue ethics using statistics. —Kyle Bennett
The error here is that there are types of arguments that don't depend on statistics.
For example, if one were to argue "more concealed carry licenses lead to less crime", one could point to John Lott's studies and statistics as evidence.
But if one were to argue, say, "murder is wrong", there is no statistic that could help or hurt that point; it can be argued entirely without statistics. (From SelfOwnership, for example.)
The two types of arguments/facts are referred to as "a priori" and "a posteriori".