Reasons to Homeschool

Having homeschooled two of my four children for one year at a time, on three separate occasions, I can only comment on how I reached that decision. Ultimately, in each case I felt I could let my child have a year in which to build confidence and mastery of skills without being smothered by the expectations of the educational system, and also to allow them to mature and gain perspective about peer pressure and the culture of the classroom. 
This strategy worked for the stated objectives. However, caution is offered for the parent of a child who may have even slight attention deficit or the old fashioned problems of daydreaming and procrastinating. Let them play and draw as much as possible because there are many opportunities for learning and discussion even in this. Their creativity will want to take wing but may need oversight. Homeschooling gives the parent a chance to really know the child and to guide them in ethics, morals, and cultural sensitivity. 
Finally, expect to spend at least two quality hours a day with the average child on the actual mechanics of either math or language literacy. In addition, the child will naturally read alot if so inclined, so certain children have no problem getting the content down for social science subjects, history, et cetera. Be prepared to give them lots of homemade challenges--make your own maps, plan trips, include the child in shopping and enjoy applied math lessons. Talk about current events to teach geography, science, and social studies, and to have priceless discussions about ethics and citizenship.
Children who are not comfortable reading on their own, or who seem to avoid it, may need professional tutoring or even clinical evaluation to identify learning disorders, but don't hurry into this. Female students generally read earlier than males, who may not want to read before age eight due to emotional immaturity or nervous system immaturity that affects attention span. While girls are rumored to have math anxiety by middle school, I can personally assure you that it can be a problem much earlier due to a teacher communicating her own math anxiety through her personality in the classroom. If one or both parents are available daily to work with the student in a loving, relaxed atmosphere, the results will be positive--far more positive than the child continuing to be humiliated by a sense of lagging behind others in the classroom simply because they have an emotional block.
I have also homeschooled a gifted child, but this child was also ready to return to the public school after a "boring" year. The homeschool model may work best where there are siblings and also friends or other homeschooled children for socializing. Regardless, if you are not a totally neurotic, short-tempered parent, you may be a better teacher than the one your child would have next year, so I would encourage you to consider spending a "together year" if you are academically qualified, which is not to exclude those who are self-educated at the exclusion of university level degrees. 
Most school systems require that your pre-apply to gain approval to homeschool for the following academic year. They may require you to use approved materials, which may be quite expensive, or submit written curriculum for school administration approval. They may require you to have a four year degree yourself or submit to closer scrutiny (for example, by using pre-approved teaching kits, which you may be able to buy at a used price.) Students are generally required to test at least once during that academic year to be sure they are at or near grade level. Those who don't meet grade level after one year may still have gained in self esteem and emotional maturity if the homeschool environment was healthy and supportive and the parents patient and accepting of the child's individual style of learning. Most homeschoolers without pre-existing learning difficulties actually outperform their peers in classrooms. 
Call your local school system administrative division for state and local guidelines on homeschooling in your state and county in the United States.