This idea is also completely foreign to me but I have heard of a lot of hunter/jumper barns being the ones that have your horse all ready and tacked up for their students. In my experience, many hunter/jumper barns have very strict, set schedules for their horses and you need to follow them in order to maintain their "like of riding" or something like that. Maybe this is the case at your barn? If it is, try asking to learn how to tack up an older retired horse in place of your lesson. This way it doesn't still have the set schedule because it's retired but you are still able to learn how to tack up.
At my barn, I'm the one who helps teach the lesson students how to get their horse, tie it up, groom it, tack it up properly, how to check the saddle, and just in general how to be around horses. The saddles are always checked before the student gets on, as well as the bridles. Their first lesson is primarily learning how to do everything before getting on and explaining what their tack is and how it functions, as well as a few parts on the saddle and bridle.
I agree with everyone that just asking won't hurt anything and that eventually, it's something that you should learn, but maybe your instructor doesn't feel you are ready for this step, yet.