To me it does make sense. The begin point is the first mentioned, if I say "between 10 and 100" ten is the begin point and one hundred the end point while if I say "between 100 and 10" one hundred is the begin point and ten the end point. Since the whole thing is non-directional, between-ness doesn't take account of which is the begin point and which is the end point, unless it has different preferences for inclusion of the two points, and since you have a different degree of preference for the two it's clearly essential that you distinguish between the two. That certainly makes sense - at least, to me. Your distinction between the two points may not work the same way as mine, but to me, at some level, that doesn't matter - we both make a distinction; it may have different consequences for each of us, but the fact that there is a distinction allows each of us to assign consequences. Of course at a more detailed level we may disagree - or not.

edit: change /quite to /quote