Callouses are Mother Nature's way of protecting your skin when you do hard work. Your strings are made of wire, and the action of pressing your fingers against a taut wire can be a little irritating to your fingertips. Most people eventually develop protective callouses on their fingertips, and beginning musicians often find them very annoying.
I will try to put this in perspective for you by telling you that serious musicians often go to extreme lengths to keep their callouses as hard and as thick as possible - even going so far as to shower with rubber gloves on so that the hot water does not accidentally soften them. In the course of playing, many experienced musicians slide their fingers along the strings, quickly, and that action could actually slice open their skin if it were not for the protection of their callouses. There's also a certain honor in being able to stand in front of a group of musicians, scowling at your fingertips and saying, "My callouses are killing me" - because that means that you must have practiced a lot more than they did.
My advice to you is to leave your callouses alone and, in fact, do your best to keep them there. If your skin flakes off from the fingertips, that's a little different because the dead skin will corrode your strings and shorten their playing life. Some people get rid of the dead skin (not the callouses) by rubbing either a pumice stone, or a fine grade of sandpaper on their fingertips. I rub a good moisturizer in to my fingertips after I practice (I'm partial to Aquaphor ointment), and that seems to take care of the dead skin problem for me.