Overall, homeschooling eliminates the pressure that public schools put on kids to fit into a mold of what they're learning and test scores and the like. Homeschooled children are given more freedom on the subjects they learn, and here in the US with the cutting of programs for music and arts those kids can still learn those things if the parent wishes. Homeschooling also teaches kids to be independent at a very young age as well.
I don't agree with some other answers here that a child would stop taking learning seriously or have no challenge because there is no comparison to others; quite the contrary in fact, as for many public school takes away the joy of learning and it's why many people stop learning as adults because of how they were taught and how it is no longer enjoyable thanks to school. And constantly comparing yourself to others or being compared to others just kills self-esteem and makes one think they are never good enough because there is always someone who will surpass them, which can cause anxiety in children. If the material becomes too easy when homeschooling the parent can always choose to give them more advanced subjects to study.
I also don't agree that there's no one to be accountable to with homeschooling, as the children are still accountable to their parents to complete the tasks of school. The problem comes if the parent does not hold the child accountable, and that's strictly on the parents who then should not be homeschooling the child instead of on homeschooling as a whole. Also learning to be accountable to yourself before you're accountable to a teacher/parent/boss is a good life skill, especially if the child goes on to run their own business or freelance or something similar.
The downside, however, is that social skills can sometimes become lacking unless the parents take steps for that. There is nothing wrong if the child feels anxiety and is most comfortable keeping interactions to a screen or video/voice chat because some people are naturally introverted or sensitive to other people and would want to keep their distance, but until that really starts to present itself the parent needs to be responsible for making sure their child is socialized. Get them involved in a sport or some kind of other group or club they're interested in, that sort of thing. But of course children can be very mean to one another and some might mock the child for being homeschooled which is something that will have to be dealt with as well.
But overall public school is expected to be a one size fits all for every child and that's just not possible. Some children learn by listening, others by reading and still others by doing. Some have learning disabilities, or mental disorders like anxiety and depression that a public school environment does not recognize, will make worse, and/or will only do the bare minimum to attempt to help and then will berate these children for not being like the others. With the advent of technology making it so much easier I can see why many parents are choosing to take their children out of such an environment and homeschool them instead.
