Is it normal that i can't stop drinking?

If one is an alcoholic, they are and alcoholic even if they aren't drinking. It doesn't matter if they are honest or not; they are addicts.
One does not EVER stop being an alcoholic if one is an alcoholic. They can only choose not to drink, but there is no cure.

To the OP: Only you can ultimately decide if your drinking is a problem, and what you need to do about it. I'd suggest you find an Alcoholics Anonymous meeting near you (there will be one, and probably quite a few, wherever you live). Go, and just listen. No one will make you talk or commit to anything. Just hear what others have to say, and think about how it relates to your own experience. There are even online meetings. All of it is free, safe, and no strings attached. At the very least, it's worth an hour of your time to find out more about it.

To the Gypsy Sailor:
Not one of those statements is 100% true as written, and the first paragraph is almost completely false. In fact, no one is certain of exactly how, when, or why a given person becomes chemically dependent (an "addict") in the clinical sense. Experts agree that once this threshold is passed, the condition is chronic, progressive, and currently irreversible. Its progression can be halted by taking certain measures (e.g., discontinuing use of the substance & adhering to a proper treatment plan), and these must be maintained for life to prevent relapse. If they are, the person is a "recovering addict" (or "recovering alcoholic," if you insist on upholding the outdated, baseless, and absurd differentiation of alcohol from other psychoactive drugs). They are still an addict for the rest of their life, and without ongoing effort at recovery they WILL return to active addiction, so your last statement is technically true.

However, the distinction between active and recovering addict is like night & day. It is important -especially for addicts & those around them- to stress this because without it, many people hear "addict for life" and think the hell that is *active* addiction will last forever. This breeds hopelessness, which in turn keeps people from even attempting the difficult road of recovery. It makes both addicts and families far less willing to reach that critical first step of admitting that there is a problem. So your last statement is, at best, entirely unhelpful. The way it sounds to someone who is -either directly or indirectly- struggling with this is: "It's fine if you keep this all to yourself, just so long as you realize that you're completely f-ed, and always will be!" Addicts and families would be better served by realizing that if you take away the stigma, addiction is very much like type 2 diabetes. Both are devastating and terrible if left untreated, but both CAN be treated. In both cases, treatment usually requires substantial and difficult lifestyle changes since, in both cases, lifestyle choices were a major factor in developing the condition. Perhaps this medically-accepted and far more relatable phrasing might be better than, "You're a bum- you were born a bum and you'll die a bum!" yes?

And this brings me back to your first statements. Although there is compelling evidence that genetics plays a role in addiction, one is absolutely NOT "born [addicts]." Most likely, some people are more predisposed toward substance abuse &/or addiction due to family history, but chemical dependency (again, the clinical, chronic condition recognized by medical science; not the popular stereotype) requires, by definition, one having used the given chemical. The only people born as addicts are those who were exposed due to the mother's use during pregnancy, and even that is a much rarer phenomenon than the media lead us to believe decades ago.

Your second statement is even more absurd. There is no amount or frequency of drug use (including drinking alcohol) that makes one an addict. Not all alcohol addicts binge drink, drink every day, or any other popular assumption. Likewise, not everyone who binge drinks or drinks daily is, in fact, addicted. In truth, the threshold between substance use/abuse/addiction is rather nebulous, and different for each individual. Alcoholics Anonymous insists that people SELF-identify as alcoholics for exactly this reason. Only you really know if you have a problem with drinking &/or other drugs. The closest thing to a common thread is the simple question: Is alcohol (or whatever) causing problems in your life? If so, you MIGHT be an addict, and ought to think about making some changes.