Networks want the right to decide which packets they send and which they don't (right now, all packets are "neutral", sent at the same speed and priority).
If granted, it would allow networks to extort, essentially, payment from any web site, to make sure their service is accessible by its users.
Except there's little to no competition in the ISP industry right now. In my area at least, you either have Comcast or Verizon, there's no other options.
"Competition" may or may not take care of the problem. As imgabe points out the market for high-speed internet connections is an oligopoly. Depending on the specific scenario an oligopoly can be almost as efficient as a free market (competition is taking care of problems) or almost as inefficient as an unregulated monopoly (competition is not taking care of problems).
A non-neutral network is one possible outcome of an inefficient oligopoly structure of the high-speed internet connection market. If we want to avoid that inefficiency it behooves us to at least threaten regulation of the market. Hopefully the threat will be enough but if not then regulation becomes more of a requirement if one is concerned with economic efficiency.
Remember the POTS network was built-out using a government-sponsored monopoly (AT&T). If such an unwieldily structure could bring copper wires out to every rural farmhouse in the country surely the "free market" will be able to provide high-speed internet connections just as universally without having to resort to inefficient extortion of high-tech companies.
