The general arguments are the usual.
1. Homeschoolers don't believe in social interaction.
2. Parents can barely teach their kids manners let alone educate them.
3. Degrees prove competence.
I can't even begin to answer all of the asinine blather in this article. So I am just posting quick answers from my own families experience.
1. My kids interact with both kids and adults of various backgrounds, ethincities, and income levels. We interact with neighborhood children, friends from church, librarians, postal workers, etc. on a weekly basis.
2. Homeschooled kids consistently outscore public school kids in every test thrown at them. My kids are learning manners, Bible, Spanish, reading, handwriting, astronomy (planets, asteroids, etc.), biology (toad life cycle, tropical rainforest habitat, etc.), math, and art this week. While my son might be behind a little in reading, he is almost a year ahead in math. My daughter is 4 and easily doing kindergarten level work.
3. Degrees prove nothing except that you can nicely stack bologna. Bill Gates has done a fine job of running Microsoft (and now passing it on to another CEO) without an MBA or even a bachelor degree. I have a degree in Landscape Architecture with something like a 3.8 average. Big freaking deal. Probably the two most successful people in my class had a C+ average. I am just a better bologna stacker who had more free time to do a good job on projects because I didn't have to work my way through school.