Tragedy of the commons. If people owned areas of the ocean in the way they own areas of land for farming, this would be less of an issue.
Here's a list of North American fisheries, some of which are well managed: http://www.nmfs.noaa.gov/sfa/statusoffisheries/2011/second/Q...
But the basic principle is the same: private property rights can help mitigate these problems.
The optimum strategy for small land ownership is often maximum exploitation. In the case of the ocean fishing people would fish as much as possible, and just wait for more fish to wonder back.
That is, private owners in this case are able to socialise the cost of their operation, which is no more private ownership than when the profits are socialised.