It's not the ISP's job to enforce another company's copyright.
There is a city where a road service provider (RSP) builds and maintains all roads. At strategic places, there are road checkpoints where the RSP can block traffic.
Recently, there has been a series of bank robberies. The city has strange laws: Bank robberies are illegal in he city, but hard to prosecute directly. The bank, knowing who participated in the robberies, asks the RSP to block the robbers' traffic.
The RSP refuses, bank sues the RSP.
The analogy falls apart here anyway because bank robbery is a criminal offense and the police are around specifically to deal with it. Piracy is a civil offense. I don't know of any comparable civil case where a private third party is required to enforce a contract they're not involved in.
Please don't associate the violent deprivation of property with voluntary exchange violating state frameworks to promote intellectual publication. It is disingenuous to the argument and hurts arguments on both sides of "piracy is bad". If a company is an enabler of violence and actively work to intentionally promote it, of course they should be liable for their behavior.
Your sentence
> If a company is an enabler of violence and actively work to intentionally promote it, of course they should be liable for their behavior.
doesn't respond to anything in the parent comment you're allegedly replying to. No one is saying, or thinking, that road builders work to promote robbery by road users. What they are saying, correctly, is that road builders are enablers of violence that otherwise wouldn't occur (ever heard of "highwaymen"?). They're also enablers of more useful, fruitful, and desirable phenomena.
> doesn't respond to anything in the parent comment you're allegedly replying to
Except it does. You say yourself, banks would have a better case, but when you say it out loud it sounds absurd. The only time a business is an accomplice to bank robbery is when they are intentionally promoting it explicitly, but when their business enables it. To degrade that argument to civil conflicts and then claim ISPs are responsible for their users is more ridiculous.
Hey, what a funny coincidence. If only there were some well-known style of argument with such a feature.
It could be called something like http://en.wikipedia.org/wiki/Reduction_to_absurdity
You seem to have confused an argument against ISP liability for customer behavior with an argument in favor of the same.