I get to spend time with my kids when they are at their freshest. Instead of seeing them mostly as they rush to go off to school, and when they come home cranky and stressed, I get them when they are at their best..and also, of course, at their worst....
My husband gets to spend time with them because we can adapt our schedules to him. He usually works from 10am to 7:30pm, and this means that he would see them for only an hour or so before they had to go to bed. So much for quality time with daddy...
I get more time to play with Legos, and read my favorite kids' books without having anyone accuse me of being childish.
The schools usually frown on kids arriving late or skipping school to sleep in after a very late night of astronomy...
The snow here in our part of Ohio only stays around a few times a year. Most of the time, it melts before lunch. My kids can play out in it, but most kids are in school and can only see it out the window...if they actually have a window in their classroom.
Since I brought that up, I'll make the fact that all our rooms have windows part of the list.
If the air conditioning at our house breaks, we can get it fixed without a new tax levy and three years' time, unlike a school near us, where kids had to go to school in 90 degree heat with few windows that opened.
More time for physical education...which is important for health.
Family vacations can be taken during the off season, which can be cheaper and less crowded.
Kids are still able to look adults in the eye. That seems to be a common statement about homeschooled children.
We help bring up the usage rates of libraries, museums, zoos, etc. with our frequent visits.
You'll get to hear a lot more of your children's original thoughts.
No long, drawn out bus trips.
One day, your thirteen-year-old will gather some neighborhood tweens and teens for a trivia contest with a new deck of science trivia cards. The winner will be your ten-year-old. Second will be your six-year-old.