Basically since he was called a moron he wants to have a cage-match battle-of-the-IQs against Tillerson now. Trump seems to have a huge insecurity about his IQ vs eggheads. He's challenged people before claiming to have the "highest IQ" but nobody's ever taken him up on the matter. He's been going on about it for the last 20 years, never produced a single IQ test result to back it up.
It's also telling that he has a moron's understanding of IQ. It has never been a test of intelligence in the normal use of the word, and it loses predictive power rapidly once you get much above average. It's designed (at least in its modern incarnation) as a diagnostic tool for people with mental difficulties, to measure how easily someone can do particular types of tasks relative to others. In that limited use, it works well in concert with other diagnostic tools for figuring out how to help people.
Intelligence is not a number, and only people without much of it think that it could be. There's certainly no way to create some kind of "IQ contest" whose results would be at all reproducible, as everyone but Trump knows.
But then, that's not the point, is it? Trump fears the results of his IQ test because the number will be lower than the biggest number the morons he scams could possibly imagine; it is even possible (or, you know, certain) that someone else's number could be higher. The reason he went after Tillerson with this is because he knows Tillerson isn't childish enough to take him up on it, so he can keep saying "and Rex was too scared to take an IQ test with me." Much like his net worth, there is no reality that will not destroy the myth.