If someone doesn't finish highschool they wouldn't be able to further their education in college and be able to get a good job with good pay to support themselves. If you don't have a job that can support you you might steal or do some other crime to get things that you need to live a good life.
It should be a law because many people believe they should just drop out because they feel like school is not needed in life. School is very useful because we need our education to be successful. Without success you get nowhere in life. With success,the sky is your limit in life.
Compulsory education through the end of high school, or at least earning a GED, should be required. Education is the way to freedom and better jobs. Whether parents, state or local governments become responsible for finishing a kid's education doesn't matter. Everyone should at least be smart enough to earn a GED before their formal education ends.
There's no reason that the government should compel anyone to get any type of education. It is simply not the job of the state to tell people what to do with their lives, including the level of education they should attain. It's the job of the parents to get education for their children until they become old enough to decide for themselves, when they will have to decide for themselves. It does not matter that education is beneficial, the state should never force anyone to get education because it does not fit the true and proper role of government: To protect people and their property rights.
No, there should not be a law that all people should finish high school, because some people are not smart or motivated enough to finish high school. Those people will become a distraction to others, and would ruin education for everyone. People who do not finish should suffer their own consequences, such as low-paying jobs.