I am only listing the pros and cons in terms of homeschooling math.
Pros: You set the pace. If you homeschool year-round you can usually skip the first third of the next math text since it is usually review. This means you can work ahead. Many homeschool kids are 1, sometimes 2, grade levels ahead. On the other hand if your child needs extra help or needs to slow the pace to understand then you have that option as well.
You know your child best and can choose the best way for them to learn. Do they learn best by doing? Then you could use manipulatives. Do they learn best by singing? Find some math songs. Do they need absolute quiet and no distractions? Then you can find a suitable place for them to study. You get to choose the methods and materials that are the absolute best for your child's learning style.
In upper level math you can take any course you like. My son wanted to learn finance and investing so we skipped Algebra II one semester and studied that instead. You could take statistics, business math, consumer math, etc.
Your kids get one-on-one instruction. Can't beat that ratio. Because you are working with them one-on-one they benefit from immediate correction. No need for them to practice an entire assignment the wrong way. You can fix problems right away.
Cons: Most of the problems are attitude problems. I know many homeschool moms that have kids that will dawdle and drag math out for over an hour. This is mostly from procrastination and distractions. Another attitude problem is a child that will whine and fuss and/or cry during math time. All of the attitude issues call for creative and consistent parenting. It can be a definite struggle for awhile.
If you don't have a lot of math training then you may need to call in a tutor or other help in upper level math.
Unless your school district has a lending policy for homeschoolers, you pay for it all...texts, manipulatives, workbooks, etc.
You may feel a lot of pressure for your kids to perform well in math. It can often feel like you and your family are under the microscope because of your choice to homeschool. This can make math stressful for you and your kids.