One criticism that I often read of Popper is that some ideas are just obvious, and so there is no need to take all this fallibilist stuff too seriously. As an example, people often say 1+1 = 2 is obvious or something like that. But 1+1 = 2 is not obvious.
Let’s start by considering the fact that 1+1 = 2 is a very abstract statement. It’s not the same as saying “I have one cow in my barn and I have put another cow in my barn, so now there are two cows in my barn.” People have been able to do this sort of thing for a long time. But 1 does not stand for a cow in a barn. It’s a number. It happens that cows in barns instantiate certain abstract mathematical relationships like 1+1 = 2, but so do peas in a pod, ducks in a pond and so on. It takes a leap of imagination to see all of those things as instantiating the same kind of abstract truth.
There is another problem, which is that the notation 1+1 = 2 is an ingenious invention. Before that notation came along, many people would use roman numerals, which made mathematical operations like multiplication very difficult. Try multiplying together 231 and 659 in roman numerals without using our current number system. Before that, there were even worse number systems like tying knots in pieces of rope. Our current notation for arithmetic makes many problems much easier.
Ideas that people think of as obvious are inventions that were created with great difficulty after many worse ideas were tried. To say that these inventions are trivial is to underrate the importance and difficulty of the problems they solve. Nor should we expect “obvious” ideas necessarily to survive because many of them will turn out to be false. Only a few decades ago, many people considered it obvious that homosexuals should be persecuted, a position that fewer people hold now. Today, most people think that children should be forced to go to school: they are wrong.