I agree you need to figure out why he won't go to school, but soon (now, probably) he will be old enough to refuse anyway and legally you can't insist. The problem is NOW, postponing things while you try to find out, probably won't help in the long run. Keep digging, but I would begin to make enquiries about alternatives. That way you can present him with the range of possibilities and get his informed input into the decision.
Are you US-based? Do you have access to any correspondence courses? We've found correspondence school to be a really effective way to manage learning at home. In Australia in the situation you describe, there would be access for your son to the state-based correspondence school.
Something else we've used, and home-school parents in our area have used, is an internet based mathematics course. For us it's A$99 a year, for 24/7 access to the software. That's a lot cheaper than the licence to another type of computer-based Maths coaching which I will not name for fear of lawsuits (we got quoted $10,000 for that system). The program also has other bells and whistles which can help.
With correspondence, the school is elsewhere and all you do as a parent is facilitate. With home schooling, you have to come up with the curriculum and make sure he does it. You write he reports, you explain his outcomes.
At 16, he is able to take considerable control of his own education. A rule we brought in when difficult child 3 spent so much time home from school (due to extreme anxiety, we found out later) was "school work during school hours". This meant that if he was home from school, even if he was home because he appeared to have a gastric problem, he still had to do schoolwork. The only way out was if he was so sick he wanted to just sleep (which meant he really was sick!)
A kid who is even a little bit motivated, often does a great deal better studying at home. You will need to work on him to maintain appropriate social interaction, but if he goes shopping with you, for example, and helps you - he will be learning how to interact appropriately in this environment, which he will need later on. Social interaction at school is vastly over-rated. When else in our lives will we be expected to sit in a room with 30 of our age-equivalent peers, with one older person in authority out the front calling the shots? School teaches you to get on with other kids, when you're a kid. But when you're an adult, you use different skills.
Anyway, that's my opinion. Home schooling ties you to your child fairly closely, but it needn't be in an authoritative capacity, necessarily. You need to have confidence, you need to be someone who actively seeks out and works on what has to be done. But there is a lot of stuff available to help you.
I'm wondering if his school phobia is due to bullying out of control. In which case, taking time out could help him regain his emotional strength to possibly return in a year or so, emotionally stronger and also older, into an older group who hopefully are more mature.
Anyway, just my couple of cents worth.
Marg