It is a one syllable difference, at most. Fif-teen versus Quar-ter-Past. Or Thir-ty versus Half-past. And for-ty-five versus quar-ter-till.

But it is also about precision. If I say “Let’s meet up at 4:45” that implies a lot more specificity than “let’s meet at quarter to five”. The firmer is an exact time people should meet at and the latter is “around that time”.

www.youtube.com/watch?v=NeopkvAP-ag goes into the difference between analog and digital time and what that means with thought processes. But a lot of it boils down to thinking in terms of “parts of a whole” versus “specific times”.