If we are talking about when the students in question are relatively young, then I don't believe they have enough knowledge to independently choose what subject they want. Furthermore, it is good to have a decent general knowledge of life. So until that point, it is best to let the child have a good general education.
Children and adolescents are usually given a broad range of subjects in a format that is considerably manageable. However, as they progress into adulthood, studies are generally more specialized and difficult. A keen interest in the subject can help students tide over the threshold to excellence, hence beget better students with good understanding and knowledge of the subject through their endurance for rigorous training. On the other hand, if students are lacking in passion, we could expect their effort to be minimal, enough to achieve desirable grades when we hope for students who are willing to go the distance, to want to understand more and will continue the learning journey in the subject for life. However, if we were to coerce someone to study a subject, it can be counter-intuitive to "what stays with you after you leave school is education"; one does not simply retain, effectively for extended periods, what one does not wish to.
I have to bring into attention words apologists opposing pro-choice may come up with. People have varying strengths, hence the contention of not allowing for choice may stem from the fact that some people pursue a subject of their desire, not the subject they excel in. The consequence is the unfortunate waste of talent. This argument, however, falls apart on two counts. Firstly, people tend to like what they are good in. Secondly, if they abandon their strongest suit for an alternative, it is likely they are positively passionate on the latter and may overcome the initial shortcomings with hard work.
By and large, not only does choosing our own subjects can give us the yearn for lifelong and deep learning, we could also nurture through zeal knowledge and skills that are indistinguishable from talent. If freedom of choice make better students, why not?
Sure it is useful to have a sound basic knowledge of all subjects early in life before it is clear which subjects they will likely make their career out of. However later on its clearly necessary for students to specialise into specific subjects that while be more beneficial and enjoyable for them. An engineer should focus on a sound knowledge of maths and science based subjects, someone who has no academic ability should be given the chance to take on practical apprentices, a journalist needs to apply them selves to the study of the language they will write in and a good understanding of what ever they want to report on.
All students should be learning the same thing in school because it would greatly help the teacher. If each student chose different subjects, then the teacher would have to plan for multiple lessons, and I am pretty sure that they don't get paid extra for preparing extra lessons. That is a bummer.
Children would more likely to focus on the short-term future rather than the long-term. If they can choose the study subjects, they tend to choose some easier subjects. For example, There are Art, dancing, singing, language, and math subject. Children tend to choose dancing and singing cos it seems easier and no homework. In this case, children lose the chances to try. If children have to study some subjects that school is chosen for them, they'll have al least the basic concept of different subject. When they have grown up and after school, maybe go to the university, they can have a clearer mind on themselves. They'll know what are their strengths and weakness. Then they can set up their future goals according to their experience in primary and high school.