Home schooling is a very good thing, if done properly. Or, it is a very bad thing, if done poorly.
To properly home school a child, one must realize what is going on in school. Children need the association. There are also various courses that must be taken--children must learn to properly read, write, and do math. There are also frequent field trips (not to be confused with field circus) and those ever-present audio-visual tools. You will be showing children videos. You will also be responsible for conducting science experiments that schools teach. And doing this usually takes a good 5-6 hours a day, plus time to correct the tests that the teachers would be doing. It also costs money.
The pitfalls often outweigh the benefits. Properly done, you can by-pass the corrupt school system. Parents should know which videos are useful (whether official or not), and which are mere propaganda videos. Materials can be adjusted--so the school uses the look-say method to "teach" children to read, you use phonics. The school uses rote memorization, you teach children to construct their own times tables. You teach children in concepts what schools teach in percepts--and get better results. And, there is no wasted time in disciplinary measures that often waste school time--how often do children spend time with their heads down because they are too disruptive?
However, if you are not careful, it can burn you. Most common is that parents underestimate the costs, and stint. This leads to crap education. They are not willing to spend the time necessary. Some parents inflate test scores, even cheating by correcting wrong answers. Some parents bias the education according to bad beliefs--which is very common among the witlesses. And, children are too-often deprived of experiences like other children, field trips not associated with field circus, play time, and the like. If you don't have the tools, you should not be home-schooling your children.
And, just what tools? Just go to any office supply store, and see what the prices of things are. You need a supply of pencils, pens, paper (lots of it), and teacher supplies. You will be printing copies of tests on your printer, or ordering them at your expense instead of having the school printing them on their own copiers. Chances are good that you will be investing in a chalkboard and chalk, or a dry-erase board and lots of dry-erase markers. You will probably need some kind of projectors for transparencies. For art, you will need crayons, lots of different kinds of paper, glue, staples, good scissors, and many other supplies commonly found in school. Music lessons will also cost you an arm and a leg (and a silver mine). And science experiments will be expensive--go into a science store and look at all the $50 and up price tags on science models. Even simple items like big screw-terminal batteries, wire, and nails can add up.
If you can afford it, if you know what you are getting into, if you are willing to spend the time, if you are going to provide the experiences, by all means home schooling is better than regular school (because you can teach fully integrated pictures whether the Rothschilds like it or not). But, if not, you are probably going to do an even worse job than the laziest, most corrupt school system.