The problem can be that most mathematics maintain that mathematics can be done for its own sake (something which I 100% agree on). However interesting mathematics is, though, there will be plenty of students more interested in the applications to the real world (and there's nothing wrong with that) or they may even have to interest in the mathematics until they see some clever ways it can be used to solve or abstract a specific problem, at which point they take a greater interest in the math itself.

As anecdotal evidence, most math teachers I had in college were at best uninterested and at worst disdainful of applying the math to the real world beyond theorems in a blackboard. Most physics teachers, however, in introducing us to new concepts made an effort to show as soon as possible how the definitions we made were inspired by real world problems and in turn simplified or helped create new physics. This made it much easier to appreciate the pure math itself.

Just explaining the pure mathmatical roots isn't always done, or cross field relations. It drives me insane when you use cross field tools, and when you bring up, Oh so we're doing X but with Y.

The response is often, No we do X because of Z. Which often you're learning Z. So now you just feel lost and confused. Its not 2 classes later until you'll learn A maps Y to Z and X is actually an operation of A so it applies to both.

I guess it's just me but the joy of math has always been its tangled relationships to itself.