If you are an adult and can pay for your own living expenses, its not wrong. But if you are still a minor-under 18, life will be tough for you. And if you are a female, it's even more scarier. Try to work things out with your parents. Best of luck to you.
Girl...it is hard enough when you actually have a family...without, the wrong types surround you, and it would truly be a very very hard road. Believe me...family, no matter how dysfunctional it may feel they are, or how hard you may feel they are on you...whatever is done, is done for love. Please, stay home, if you have issues, please get help, talk to someone!
Don't be so petty just because you get into a little fight with them doesn't mean you run away. Now if there are serious problems, such as they are abusive, you should call the cops. To answer your actual question, it is dangerous. You will have no where to go, and running away typically means quitting school, which leaves you with no future
some kids do not have homes. Some kids do not have parents. Some kids parents abuse them. Some kids have diseases. Some kids houses burn down. Some kids live in foster homes or are abused by their parents. If you run away you will have to earn your own living, find shelter food and water. You will most likely. will end up back at your house in the next week or be starved, deprived of heat. dead or worse. My friend always got in fights with his parents, and he was going to run away but i convinced her to talk to a counselor about it. He now lives with my family during the week and visits his parents on the weekend. My cousins friend was found dead after running away. It took them 11 hours to realize she was gone and 20 hours to find her dead. Make the right decision and get help, even if you dont feel like you can. And if you dont get help, then find something to occupy your time and forget about the urge to run away. Trust me. Good luck.
Most that do don't finish school, don't have a safe place to stay, and take years to accept themselves responsible for their losses. You would be lucky to find employment. There is nothing right about leaving home without a safe trustworthy place to go while you finish becoming an adult.
Talk to another trusted adult in your life right away. Aunt uncle, older cousin, priest, minister, school nurse... You can become very vulnerable and hurt by mean people if you are out on your own. Please listen to the other advice here as well.