There are many students who either can't, or don't want to, learn mathematical intuitions or explanations. They prefer to learn a few formulas and rules by rote, the same way they do in every other class.

Former teacher confirming this. Some students are willing to spend a lot of energy to avoid understanding a topic. They actively demand memorization without understanding... sometimes they even bring their parents as a support; and I have seen some of the parents complaining in the newspapers (where the complaints become very unspecific, that the education is "too difficult" and "inefficient", or something like this).

Which is completely puzzling for the first time you see this, as a teacher, because in every internet discussion about education, teachers are criticized for allegedly insisting on memorization without understanding, and every layman seems to propose new ideas about education with less facts and more "critical thinking". So, you get the impression that there is a popular demand for understanding instead of memorization... and you go to classroom believing you will fix the system... and there is almost a revolution against you, outraged kids refusing to hear any explanations and insisting you just tell them the facts they need to memorize for the exams, and skip the superfluous stuff. (Then you go back to internet, read more complaints about how teachers are insisting that kids memorize the stuff instead of undestanding, and you just give up any hope of a sane discussion.)

My first explanation was that understanding is the best way, but memorization can be more efficient in short term, especially if you expect to forget the stuff and never use it again after the exam. Some subjects probably are like this, but math famously is not. Which is why math is the most hated subject.

Another explanation was that the students probably never actually had an experience of understanding something, at least not in the school, so they literally don't understand what I was trying to do. Which is a horrible idea, if true, but... that wouldn't make it less true, right? Still makes me think: Didn't those kids at least have an experience of something being explained by a book, or by a popular science movie? Probably most of them just don't read such books or watch those movies. -- I wonder what would happen if I just showed the kids some TED videos; would they be interested, or would they hate it?

By the way, this seems not related to whether the topic is difficult. Even explaining how easy things work can be met by resistance. This time not because it is "too difficult", but because "we should just skip the boring simple stuff". (Of course, skipping the boring simple stuff is the best recipe to later find the more advanced stuff too difficult.) I wonder how much impact here has the internet-induced attention deficit.