I notice that people will use "of a"/"of an" when describing a quality of something, rather than "a"/"an" alone. I would only add the "of" in a quantifier. In my personal experience, it's more prevalent amongst American English speakers, which is supported by Ngram Viewer: British English and American English. It appears not to be dominant in either dialect.
Some examples:
It's not that big of a deal.
vs.
It's not that big a deal.
and
He's not that good of an athlete.
vs.
He's not that good an athlete.
I see it as bad grammar but am I wrong? In a quantifier it feels natural, e.g.:
They didn't provide much of a meal.
People keep suggesting this Q & A as a duplicate but, as per my comment below, they are asking why there is a difference. I have already established that the difference is between qualitative and quantitative. Thanks for the downvotes, though.