As we know, the USSR and the US were not the best of friends. During the break up of the Soviet Union, the US was the first country to recognize Kazakhstan as a sovereign nation. Why was this? My hypothesis is that the US wanted to support the independence of the leaving republics like Kazakhstan because it would further weaken the USSR which would be in the interest of the US.
In general over the course of 1991, the H.W. Bush administration was not in favor of breaking up the Soviet Union. Gorbachev was seen as a reliable partner for the US, and President Bush had gone so far as to give a speech to the Ukrainian Rada (parliament) in August warning them of the perils of secessionism and nationalism.
But by December the situation had changed drastically. A coup by communist hard liners against Gorbachev had been foiled, but the Russian President Boris Yeltsin emerged as the most powerful political force, banning the Communist Party of the Soviet Union, seizing its assets, and forcing Gorbachev to appoint his favored candidates to Soviet governmental posts.
On December 1, Ukraine overwhelningly voted in favor of national independence, and the Ukrainian government had no interest in maintaining membership in a Union. On December 8, Yeltsin and leaders of Ukraine and Belarus met at Belavezha, and signed an agreement annuling the 1922 Union Treaty. On December 21, 11 soviet republic's met and signed the Alma-Ata Protocol, dissolving the USSR and replacing it with a much looser Commonwealth of Independent States, effective December 31.
In the meantime, Kazakhstan declared its independence on December 16, the last Soviet republic to do so. Yeltsin seized control of the remaining Soviet governmental agencies and brought them under his authority. By December 25, Gorbachev was effectively a president without a state or government, and resigned, turning all his power over to Yeltsin.
Bush recognized Kazakhstan's independence on December 25 in an address to the American people. The recognition came ten days after Kazakhstan's declaration, and frankly was not a move against the USSR as the USSR didn't exist at that point. If anything it was a belated recognition of events that had been driven forward by republican leaders in the now former Soviet republics.