Personally, as a 14 year old I believe a teen at said age should be allowed to work. I understand that the law may be different in other states, though here in California it is legal. As long as the teen has decent/passing grades in all classes, work does not effect their time during school hours, and they are responsible enough to obtain and maintain their job, I don't see why they shouldn't have the ability to work.
A 14 year old should not be allowed to work at a young age, because they are experiencing a period of immense mental and physical growth, schoolwork, and additional challenges. The adolescent mind is rapidly expanding and evolving during this period of growth. By working, you are limiting their potential by limiting their time for other activities. The monetary gain that could be had in terms of scholarships, additional opportunities, and progress that is achieved by 8 hours of study is tremendous. However, the monetary gain that is achieved by 8 hours of work is almost nonexistent compared to the benefits of study. In addition, a young adult has the rest of his life to work. If you started working at the age of 15, you would have 50 entire years of work ahead of you. These teen years are best used to play sports, learn instruments, read books, and expand your mental and physical capabilities in preparation for a real job someday. Overall, a 14 year old should not be allowed to work at such a young age because the benefits of short-term monetary gain do not outweigh the benefits of the long-term gain that could be had.
Though it's true, a 14 year old needs many hours to do homework, study, play sports, and do other healthy activities that expand their social, physical, and mental health, many of them have struggling families in which they need as much income as they can get. One member of a family can make a difference with even a small income. Working is also a great learning experience for the 14 year old, giving them a taste of life after school, along with knowledge and better information for future work and/or college applications. And a 14 year old can make room for work, with or without after-school extracurricular activities, clubs or events. They can work their schedule around so they can participate in both areas. If the 14 year old meets work requirements and aren't affected deeply by this situation, then they should be allowed to work.