A lot of countries have laws saying you need to be in education until a certain age. So you wouldnt be done with school quicker. The quality of teaching in homeschooling is often lower as well as the teacher often goes through a far less scrutinous job application process.

Also unless the child is doing extra curricular activities they will not be socialising with other children, andthey will inevitably be socialising less than an equivalent child at a public school, which can be unhealthy. The chance of a homeschooled child becoming anti social is higher than that of a public school child for this reason

I've found in my personal experience that homeschooled kids are most of the time socially stunted. They don't spend time with their friends from school so they meet them online - pushing them into communities like deviant art and anime subreddits (the social abilities of most these people are needless to mention(typical social outcasts)).