My late father always used to say 'There are two reasons for everything: the good reason and the real reason.'
So I will be quite honest and say that the real reason we chose not to homeschool is because my wife point-blank refused to countenance the idea.
At the time, she wasn't Catholic; but even though she was received into the Church some 15 years ago, I think her refusal would be as strong.
However, with hindsight, there are some good reasons for not homeschooling (as well as many excellent reasons for homeschooling - some of the best Catholic young people I know have been homeschooled, and all that stuff about not being socialised is rubbish, in my experience).
However, I do think that there is some value in having children in schools who are Catholic; it opens the eyes of friends and teachers - and even sometimes those who are hostile to them - to the fact that it there are still believing Catholics about.
Ant and Bernie have both survived school and gone onto University with their Faith intact - and one of Bernie's friends is now keen to convert.
Charlie and Dominique both seem secure in their Faith, at present; and as regular readers will know, I have recently had to take the opportunity to educate their school about some basic issues...
So while I was disappointed at Anna's refusal to consider homeschooling, if I had my time again, I am not sure I would want to homeschool: for our kids, the other option has worked, and possibly benefitted others beyond our family.