Peering agreements are established between different networks to further the common interests of both network providers.
For example - Cogent and Verizon reach a peering agreement of 100 megabit. This is a dedicated symmetrical connection between the two companies. They do this because in theory it is cheaper to swap data directly rather then pay a 3rd party to transmit the data between the two networks.
Now what happens when Cogent goes and sells a bunch of cheap bandwidth to various providers like Netflix and begins flooding relatively one way traffic onto Verizon's network? Well they saturated the 100 megabit connection in one direction. Verizon who isn't anywhere close to the saturation point on their side says hey if you want more bandwidth you have to pay for it because we're not using anywhere near what you are and these agreements are supposed to be fairly equal with respect to traffic flows.
Level 3 and Cogent are both guilty of selling cheap bandwidth to internet companies who mostly only send traffic one way. Video, Music, etc... You can't expect the other side of the peer to just keep expanding the circuit to accommodate your horrible business model.
I'm not a huge fan of any of these companies Verizon, Comcast, Level 3 or Cogent but Level 3 and Cogent are both in the wrong given their current agreements and since they can't reach a deal in private they are parading this out in public and trying to make a spectacle.