To protect the USA from rogue states was the reason given by President Bush.
In his announcement President Bush said:
I have concluded the ABM Treaty hinders our government’s ability to develop ways to protect our people from future terrorist or rogue-state missile attacks. (source1)
He provided a fact sheet that states:
Today, the United States and Russia face new threats to their security. Principal among these threats are weapons of mass destruction and their delivery means wielded by terrorists and rogue states. A number of such states are acquiring increasingly longer-range ballistic missiles as instruments of blackmail and coercion against the United States and its friends and allies. The United States must defend its homeland, its forces and its friends and allies against these threats. We must develop and deploy the means to deter and protect against them, including through limited missile defense of our territory. (source 2)
In the formal diplomatic withdrawal notice, the USA states:
Since the Treaty entered into force in 1972, a number of state and non-state entities have acquired or are actively seeking to acquire weapons of mass destruction. It is clear, and has recently been demonstrated, that some of these entities are prepared to employ these weapons against the United States. Moreover, a number of states are developing ballistic missiles, including long-range ballistic missiles, as a means of delivering weapons of mass destruction. These events pose a direct threat to the territory and security of the United States and jeopardize its supreme interests. As a result, the United States has concluded that it must develop, test, and deploy anti-ballistic missile systems for the defense of its national territory, of its forces outside the United States, and of its friends and allies. (source 1)