Your parents are being lenient
I'm not sure where you live, but in the State of NJ, the penalties for underage drinking are a fine between $500-$1,000 and imprisonment for up to 6 months.
You've indicated that you've been coming home multiple times drunk, but not on school nights (which suggests that is relevant at all). Your parents would prefer you're not coming home drunk at all.
Your parents have expressed their concerns about your drinking and insisted that you stop. You did not and were brought home following being arrested by the police. This tells me 2 things. The first is that you're not able to control yourself with regards to alcohol, I don't know if you're an alcoholic or very susceptible to peer pressure compelling you to drink but you can't seem to control yourself. The second thing is that the police apparently released you to the custody of your parents as opposed to the district attorney for prosecution (WHICH THEY ABSOLUTELY DID NOT HAVE TO DO).
Focusing upon that second element, had the police instead brought you to the DA for prosecution it likely would've been a very easy case to prove and if you were in the State of NJ, you'd have faced a criminal charge. So let's look at what happens then:
- You or your parents would need to hire a lawyer (they're not cheap).
- You would have been arraigned before a judge who would have asked, "How do you plead to the charges?"
- Regardless of the answer, the end result based on the available evidence would have been that you're guilty.
- Then there would be a sentencing phase where you'd have received a fine of at least $500. And you might have been sent to juvenile detention for up to 6 months.
- Going forward, the conviction would be something that can show up in public records when people search for public information about you, which might cause you problems when applying for a job.
So last I checked, your parents aren't making you pay for a lawyer to defend you in open court, just spitballing that probably would have cost at least $1,000. Your parents aren't creating a public record of the events that occurred that you'll need to explain to potential employers for the next 20 years. Your parents aren't making you pay a fine of at least $500. And finally, your parents aren't making you stay in your room with every movement under strict control for 6 months.
Your parents are trying to get you to control yourself
I do not think you have much control over yourself when it comes to drinking. Now I want to be clear, I'm not an expert on alcohol, I've been at most buzzed a bit but never full on drunk. The primary reason for this was because my mother was an alcoholic and it was not easy for her to quit; I don't know the exact terms on how her rehab occurred but I'm not entirely sure it wasn't compelled. Knowing this about my mother growing up, I chose to generally avoid alcohol but also because I rarely like the way it tastes.
From what I've read, I do not really think that you will stop drinking of your own volition. As such, your parents are imposing a significant penalty upon you because the other potential consequences of your behavior are actually far worse.
The first concern I'd have is DUI, which I need to be clear is not a joke (seriously not even once). You can't seem to stop yourself from drinking when you go out, how likely are you to ride in a car where the driver was drinking or you drive yourself after drinking. I'm 39 myself and used to know 3 different people who have been killed because they were driving under the influence. On at least 2 occasions in my teenage life, I was nearly killed by others driving under the influence (or at least I assumed because I can't imagine another reason one would do 80 in the wrong direction). The kinds of accidents in DUI are not usually minor. And furthermore, DUI does not just affect you, there's a whole other person or family in that other car who can be hurt (often severely) by your actions; and what's more they have family who will feel the loss as well.
The second concern is long-term alcoholism. As I mentioned earlier, my mom was an alcoholic. She wasn't much on keeping up with her responsibilities around the house, she'd hide bottles around the house to keep my dad from removing them, and she'd be generally depressed for long periods of times. This was less than ideal for a small child to be growing up with.
Right now, your parents are trying to protect you from the worst consequences of your actions. Being grounded for a week in your room is far better than the legal consequences which involve much more money and time incarcerated, or the lifetime of guilt associated with knowing your actions killed somebody in a car accident, or losing your job because you were more focused on finding another drink and financially imperiling your family.
I get that you're 16 and think you know everything. This is fine, but I do think you're underestimating the consequences of your actions since you've yet to demonstrate any semblance of control for the drug that you're using.
EDIT (RESPONSES TO COMMENTS):
Given this answer has generate a lot of comments, I'm inclined to simply address them all herein.
- The application of US laws vs any other jurisdiction is partially because of my own US mindset, but also because I needed to have a basis upon which to demonstrate the legal ramifications of the querent's behavior. If you are getting drunk in Germany at 16 where it's legal, you're likely still subject to penalties by the judicial system if your drunken antics rise to disorderly conduct, property damage, and other misdemeanor type offenses. Take the penalties for those offenses from those jurisdictions and input them into the answer and it probably doesn't change.
- Regarding the comments about the morality of locking someone in their room, I've 2 general sentiments on this. The first is that the question asked if the parents were 'right' to give the querent a severe punishment after being brought home by the police for behavior the parents expressed concern about prior to this; I would argue that a severe punishment sends a message that hopefully is understood. Note that the querent is not being denied food, water, or even entertainment, they are being denied freedom and were they subjected to the judicial system would likely lose a lot more freedom. The second sentiment I have on this is that assuming the querent is addicted to alcohol then the appropriate solution might end up needing to be something like rehab where again all your movements and actions are pretty controlled. If the response to this suggestion is that then the parents should do rehab, I would caution that such a course of action is easier in some places than others; but for the US that entails a lot of money and probably a lot of PTO (which the US notoriously doesn't provide), so such a suggestion is potentially ignorant of the real world complications.
- Regarding suppositions that the parents shouldn't be doing this and instead teaching the querent how to drink safely and appropriately, I agree. But for all we know, maybe they tried that already; after all they were aware that the querent was drinking so perhaps they'd given such behavior a blessing but became concerned because the querent wasn't doing it responsibly as they were taught. Furthermore, I'd wonder if this sentiment were the same if the querent were brought home following a spate of vandalism? Or DUI? Or DUI with injury? Perhaps the parents are in fact teaching the querent about responsible drinking by also reminding them of the penalties for irresponsible drinking.