Alas, "there is no such thing as market failure - only lack of private property rights." Hence, externalities are the creature of the mixed markets, those in which government has preempted the common law of liability, with its own ineffective policies, in which some cases is a form of corporate welfare (logging industry, fishing rights, etc.)
Without delving further into the economics though, I'd like to state that such a claim is prima facie fallacious because the very notion that there exists an objective definition of what services and goods that billions of interacting individuals ought to offer one another is preposterous. If that weren't true, I humbly submit that there is a market failure to deliver styrofoam houses, bicycles made from gold, and teleportation machines.
Thus said, there is no market failure because one cannot argue that such goods or services ought to be provided by the market, only that they, strictly on a personal basis desire the provision to be made.