Why Hello there! Out of curiosity have you ever been homeschooled? 
I've never been homeschooled before. I know that according to statistics only about 3 percent of all children in the US are homeschooled. Have you?
I have not however I've always been interested. The teacher to student ratio seems so beneficial for developing minds
Yes, it seems that on average homeschooled students score at least average on standardized tests and often above, so it may be quite beneficial if the parents have the time.
Yes I agree if the parents have the time it would be great. It's also a potential saver of money on a per student basis due to not having to fund building and classroom environments to house many children at once
I believe though there is a downside in the loss of social interaction you get from school. Learning how to interact with many different types of people can be useful later in life.
That is a skill that children would need to learn outside of the school environment if homeschooled. Could you potentially foster that same social interaction through after school activities such as sports/band? 
Yes, I think so if the child is interested in such activities. The benefit of public schooling would simply be that the child has these interactions on a reliable and constant basis. It is possible homeschooling can lead to social inhibition which includes anxiety in interactions and avoidance in social situations.
True but who is to say that the factors of anxiety and other mental/social issues wouldn't arise from a particular student regardless of environment. A genetic disposition if you will 
That's true. Anxiety disorders can be caused by both genetic and environmental factors. Social isolation from homeschooling may trigger this though.