It takes a good amount of time. Two hours a month is not much. I have been riding for almost six years now on and off and I have been taking lessons consistently for almost two years now. I still have a lot to learn. There are MANY things that you need to learn in order to own a horse and trust me right now it probably seems easy because you're just doing somewhat beginner things and probably riding a beginner lesson horse.
Non riding stuff:
*Vices and how to recognize, fix and/or control them.
*Common injuries and how to treat them and when to call the vet.
*How to tack up quickly and efficiently in your chosen discipline..
*How to groom.
*How to feed and water a horse correctly (this is useful to know even if you won't be doing it yourself).
*How to actually BUY a horse! There are many things to remember so you can have the best possible buying experience and get the proper horse for you, such as bringing someone who KNOWS horses with you, getting a vet check, etc.
*How to lunge a horse.
*How to lead and halter a horse (easy but...still lol).
*How to put a fly mask on.
*How to put a blanket on.
*How to find the right length for your stirrups.
*How to hold the reins.
*Being able to post, sit, and extend the trot confidently with and without stirrups. Be able to at least post/sit to the trot bareback, wether you decide to post or sit depending on the horse's trot. Getting the right diagonals while posting.
*How to canter, preferably both in the arena and on trails as well as without stirrups.
*How to jump at least small cross-rails. You never know when a horse may decide jumping over random things is a good idea.
*How to control a bucking horse.
*How to control an otherwise moody, misbehaving horse.
And it goes on. As for how long it takes to learn everything...depends on the person, of course! But for posting, it took both me and my cousins several months to really get our posting to a nice movement we don't really have to think about. But I'm not sure there's a point you don't have to think about where things are. Even my instructors say they still forget to put their heels down every now and again! So it's really just a "practice makes perfect" kind of thing so that you don't have to think about everything constantly.