Dad What FurryDog says is correct.
One can't have "another thing" without having first had a thing.
The phrase means "think again"! For example, something my father often used to say to me is "if you think I'm going to let you go out dressed like that, you've got another think coming!"
It simply wouldn't make sense to say "if you think something, you have another thing coming. What was the first thing? As I said, one can't have another of something if one hasn't yet had the first one!
The use of "another thing coming" has only come about because people have misheard the word "think" as "thing".
It can happen quite easily. I confess that I was well into my 20s before I realised that the phrase "he did it off his own bat" was indeed bat and not back, as I had been saying for decades! My parents had said back , which is wrong, and I assumed that's what it was supposed to be, until I was reading a book where a character used "bat" - and I realised of course that I (and my parents) had been saying it wrong all along.
There's no shame at all in getting it wrong (thing sounds very similar to think and it's an easy mistake to make) but I do think that one should have the good grace to accept that one is in error, when that is clearly the case.