Which side are you assigned to argue?
Or do you get to pick? If you get to pick I assume you’re going to argue that the Health Care Act is unconstitutional, or at lease this particular provision is.
Based on your description of the professor I’d stick to the law & constitution, even if the other side doesn’t and argues rhetorical policy points.
Argue that Roberts was correct on the commerce clause et all but incorrect in his reading of the taxing power, as there is no constitutional authorization to tax anyone for not purchasing a good or service.
You could also attempt to argue that this is a case of uncompensated takings, as Mr. Miller will have to forfeit his license and thus livelihood. However I’m not sure how far you’ll get as courts have typically not found much of anything a government does as violating the takings clause. For better or worse you’d probably have a better shot invoking the 14th amendment’s due process clause. :p The idea is almost certainly to find case-law precedent to support your position rather than argue principle.
The other side will probably introduce arguments based on policy and costs; if so you can point out that there are costs to driving people out of their livelihoods as well.