Supporters of net neutrality have often argued that more competition among Internet service providers (ISPs) is beneficial for an open Internet and that the market power of the ISPs lies at the heart of the net neutrality debate. However, the joint effects of the competition among ISPs and among content providers (CPs) have yet to be examined. We study the critical linkage between ISP competition and CP competition, as well as its policy implications. We find that even under competitive pressure from a rival ISP, an ISP always has the incentive and the ability to enforce charging CPs for priority delivery of content. Upending the commonly held belief that when facing direct competition CPs will always support the preservation of net neutrality, we find that, under certain conditions, it is economically beneficial for the dominant CP to reverse its stance on net neutrality.