I'm teaching some syntax revision sessions yesterday and today, for students who have to resit first year syntax. Yesterday only one student came, and then one more turned up right at the end having got the time wrong. But still, the one who was there said she found it helpful so my time wasn't entirely wasted.
The night before, I tried teaching my partner how to do syntax. He has never done any linguistics in his life, and isn't even academic (he left school before he got his A-levels). Nevertheless, we thought it would be interesting to see if he could understand it.
Rather than try to teach him all the terminology, which of course you can't just learn instantly, I had him work it out logically, asking him how he would split the sentence into two, and then that constituent into two, and so on. I had him thinking about the relationships between the constituents, and what modifies what (a lot of terminology actually transfers well to real life). And he was surprisingly good at it - he got everything right, pretty much first time.
So why can't the students do it? It's partly because they get bogged down with having to learn all the terminology and what's an NP, what's a modal and so on. But it's also noticeably the non-scientifically minded students that end up resitting. We get almost all arts students doing linguistics, because they've followed on from an English language degree, and they aren't the best at linguistics. Often the best linguists are the science students, the ones who are good at maths and logic and understand relationships and hierarchies between things. That's what my partner is good at and he picked it up straight away and totally got the basic principle, which is something that a lot of the students miss completely.