My principle problem with this is pretty much as you illustrated. We can all sit down, as you did, and in a very short time concoct a list of impossible things. And if you hand that list, neatly titled "Impossible Things," to Tertullian, will he believe them? The big flaw here is that the number of impossible things is infinite, limited only by our imaginations. We can't believe them all, can we? No, of course not. So how do we choose which impossible things to believe?
Other than reason (which I assume Tertullian spurns), there is no standard to which we can turn, except pure authority. And if the authority picks the wrong impossible thing, what are we to do? Indeed, having abandoned reason (which includes observation and logic) how would we even know the authority is wrong? All we would have is faith in the authority.
That's how some people end up dead in Jonestown, and others die trying to catch the Heaven's Gate comet. It's not for me. I'll stick with reason, and if something is clearly impossible, I won't believe it. Sorry, Tertullian.
‘Can’t you ?’ the Queen said in a pitying tone. ‘Try again, draw a long breath and shut your eyes.’
Alice laughed, ‘There is no use trying,’ she said, ‘one can’t believe impossible things.’
‘I daresay you haven’t had much practice,’ said the Queen. ‘When I was your age, I always did it for half-an-hour a day. Why, sometimes I’ve believed as many as six impossible things before breakfast.’