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Discuss a possible solution. Accept their decision. Continue to have discussions.
To come to a solution, you both will probably need to compromise. That is, you parents might need to give a little, and you might need to give a little. If you both give in a little bit, you might find a solution you're both happy with.  When you're trying to compromise, you have to figure out what both of you want or need. For instance, your parents are probably most concerned with your safety and well-being. You're probably most concerned with getting what you want, such as a little more independence. Say you want to spend the night at your friend's house. Your parents may not want you to because they don't know the parents and so, they don't know if you'll be safe. You can come to a compromise where you start out by everyone going out together, so your parents can meet her parents. Then, when you do go over, you can agree to check in with your parents every so often so they know you're okay. That way, you both can feel a little better about what you want. However, your parents might be unwilling to compromise if they think you won't be safe, so think about that when trying to make a compromise. You may not get what you want. Your parents may not be persuaded by your arguments. If that's the case, it's best to accept what they have to say for now. In the future, you may be able to try again. If you whine and complain now, it will make your parents think you're less trustworthy, not more. One way to help your parents understand how you're feeling on the topic is to discuss your feelings and thoughts openly with them. That doesn't mean that you nag them constantly about changing their minds. Rather, you need to have an open dialogue about why you feel the way you do. For instance, if you're trying to get your parents to let you go out more, don't say, "You're awful. You need to change this decision." Instead, say things such as, "I know you want to protect me, but I feel really left out when my friends go out without me. I don't want to go to parties or get drunk. My friends like to go out to coffee or to the movies, and I feel like these activities should be acceptable."