The solution doesn't violate or bend the guidelines given (using four straight lines). Assuming that some strict rules exist seems to be a cultural behavior - probably ingrained from school, where doing things creatively can get you in trouble. </sociologist>
On the other hand, if you have seen these kind of problem before, you already have a hint that the solution involves something unusual.
> The solution doesn't violate or bend the guidelines given (using four straight lines).
Yeah; which is partially my frustration. The other part is that I actually went pretty in depth compared to how much time I would expect most people to go at it. (About an hour with a pencil and paper journal. Figuring out what couldn't be the solution with "You're starting from one of the dots" as an implicit axiom.) I was actually about to write a script to brute force the solution after I ran out of ideas, until I decided to save myself the time and peek at the solution.
Actually it's quite easy to bruteforce by hand if you mention that point set has multiple symmetries. For example, you only need to start drawing lines from (0,0), (0,1) and (1,1). Any other combinations are derived by rotation and mirroring. After several minutes you can prove that solution in impossible under implicit presumption that every line must terminate at a dot. And after that puzzle is really easy.
On the other hand, if you have seen these kind of problem before, you already have a hint that the solution involves something unusual.