Sounds like you are trying to arrive to predefined conclusion. Given the sorry state of public education, where schools graduate illiterate people unable to read their own diploma, if homeschooling is a sign of something it is a sign of deep commitment to the child's education. The second argument is even weaker - it sounds like if he had a lot of degrees, he'd be against education, and if he had none, he'd be against education. Solid argument needs more than that. You can see in parallel branch I am very far from being fan of Santorum, however disliking him does not mean getting to his level and starting to use prejudices instead of solid argument.
> if homeschooling is a sign of something it is a sign of deep commitment to the child's education.
Commitment to what aspect, though? Actual educational and personal development or complete indoctrination in a bubble where no outside ideas can penetrate?
My point is that it's an ambiguous indicator, and can honestly be used by both sides until we know details about the homeschooling in question.
What's "actual" education? One's personal opinion can differ. However, education and indoctrination are not mutually exclusive. The debate about mentioning creationism in schools shows that both sides see the school as the indoctrination vehicle - otherwise describing the existence of the creationist theories, which is - the existence of the theories, of course - a scientific fact would not be controversial, but there's more to it than just that, right? And educational institutions themselves are deeply political - D/R ratio in some academic disciplines is 30/1, some institutions are completely ideologically monocultural, and teacher's union NEA is 6th biggest political donor, donating almost exclusively to one party. There are also numerous documented cases of teachers involving pupils into political activities for the causes of their choosing. So it would be very hard to find an education venue where indoctrination would not take place.
The whole point of the homeschooling (one of) is that people choose what is actual education for them, not for somebody else. Of course, you or I may not like their choice, but why should they care?
> What's "actual" education? One's personal opinion can differ.
A good education is one that reflects reality. If your opinion of what reality is differs from mine, you're welcome to show me wrong using experiments. Otherwise, you are wrong and are not likely to be a good educator.
> The debate about mentioning creationism in schools shows that both sides see the school as the indoctrination vehicle
Not to the extent you seem to think: One side has facts on its side, whereas the other does not. If you can't see any asymmetry there I refuse to try to help you.
> Of course, you or I may not like their choice, but why should they care?
Because I have to live with the laws they have the political clout to force through Congress. I have to deal with the fact they have just as much political clout as I do and no idea why the tides come in or why trickle-down economics is a terrible idea or why banning abortions doesn't magically make everyone into someone who can raise a child in a reasonable fashion.
As for the number of degrees, excess can breed contempt. Also, college is a great place to have lots of sex and be exposed to tons of secular ideas.