We chose this route. I'll put a brief list together, but realize there may be others depending on your situation. We're entering year 3 of our decision. I was previously employed as a high school teacher, so I wasn't bringing in six figures. (Note: my wife is also a teacher.)
1. I love my kids, and I'm not the kind of adult that needs to get away from or take a break from them (even though it's nice sometimes.)
2. Health insurance - this is a YMMV category for everyone. With the loss of my income/job, the size of our family (already 2 kids, now 3), and the relatively low income of my wife, our kids qualified for Medicaid. Yes, people may look at this as wrong or abusing the system. For anyone interested in how this works on our end, PM me. Otherwise, chill out. (Note: I'm not covered by Medicaid, so it's self insurance for me for various reasons.)
3. Homeschooling has costs. Mostly, this comes in the forms of what you make of it. Homeschool share programs can cost some money. Curriculum can cost some money. Testing can cost money. Some of that you can or should be able to outsource to your local school system if necessary, i.e. testing, speech therapy, or some other specific need.
4. Being a SAHP does not mean no more income. I can do random things at home to make or save money during each school day and still have time to homeschool my kids ages 7, 4, and 6 months. Sometimes it becomes a homeshool lesson and accomplishes a 2-for-1.
5. No more 401(k) or 403(b) max contributions. Unless I set up some kind of SEP, I'm missing out on those tax free earnings. Oh well.