As generally framed, one side argues government ought to ban internet providers from differentiating service based on "kind of traffic or level of traffic", while the other side argues government interference will do more harm then good.
Proponents, rightfully, fear a landscape in which a few companies control information and stifle innovation. Critics, rightfully, fear regulatory capture as just as sure a path to that landscape and mock the concept of content-agnosticism:
On one side there are likely companies that dream of parlaying control of the (metaphorical) rails into control of the cargo. On the other, some Net Neutrality advocates recognize that their cause is being co-opted by groups whose agenda entails "nationalization of everything from the communications and broadcast infrastructure to the failing newspaper business."
A woman gets a pacemaker that "will wirelessly contact the hospital if she suffers from cardiac arrhythmia. Are you telling me that it would be illegal to prioritize that traffic over a video of a squirrel on water skis?"
Within a rational politics, we would be able to adopt reasonable rules: Providers would have to treat similar content from different vendors agnostic-ally, but could prioritize certain sorts of traffic (eg: emergency medical), and sensibly manage levels of traffic. Almost no-one in this debate believe that outcome at all likely.