In my experience this attitude is extremely widespread amongst university departments. I think it's a simple combination of elitism and poor training in pedagogy (unlike school teachers, university lecturers typically undergo no mandatory training in teaching).
When the author described this specific math class as a required math class for Engineering majors and not math majors, I spotted it for exactly what it is: a weedout course.
It's intentional.
Aka Institutional Gatekeeping.
Possibly the concern with sharing answers is that students could memorize the form of likely exam questions without deeply understanding the material? But that risk exists simply by sharing the questions so I’m not sure I find that argument persuasive.
I’ve always been rather disappointed by the lack of solutions in math books. I mean, on the one hand, it’s a great feeling to crack a difficult problem unaided, and there’s something to be said for building the intellectual discipline one needs to attack a problem with no easy answer.
But also, there are some problems that I never manage to solve because I “time out,” and it’s possible that as a result I’ve missed the opportunity to learn techniques that will be useful in the future.
Still, it seems there's bits of departmental strategy that are a bit kooky. Why provide practice problems (not for credit, it seems), and then never share solutions? What is the point in the student practicing without feedback about correctness? Wrong practice is just as likely as right practice.