no your teeth aren't supposed to be loose. you probably have gum disease (worse than gingivitis). flossing would have prevented it. however at this stage you probably need a scaling and root planing.
to remove all that calculus (hardened plaque) from under your gumline which makes the gum not stick to the tooth anymore which is a likely reason why it's loose.
and now i'm going to go floss like i do every night having had that scaling & planing once inflicted upon me. my teeth weren't loose yet at that point and all my deep gum pockets fully returned to normal since i started flossing every day.