After 2001 when Taliban Government fell then there was a question of who (and more importantly how) will rule the Afghanistan? So, there was a conference in Bonn,Germany. Hamid Karzai was appointed the chairman of interim administration. Later he won the election of 2004.
However, Hamid Karzai had some contention with the USA. He always wanted USA to take harder actions against Pakistan. In his viewpoint Pakistan was nurturing terrorists. Yet George W. Bush made Pakistan a 'major non-NATO ally'. Karzai said in an interview,
They have blamed Pakistan in the past as well for nurturing
sanctuaries — Obama did, Hillary Clinton did, their defense
secretaries did. They blamed Pakistan but kept bombing Afghanistan
Another point of discontentment was USA (and coalition) didn't care about Afghan lives. In his viewpoint,
This is an unending war where we die. We Afghans are being used as
cannon fodder, as ammunition. ... They would say that they want to
fight the Soviet Union to the last Afghan. They want to pursue their
interests at the cost of every last Afghan. We don’t want to become
the battleground for the U.S.’s objectives in this region, but that is
what it is going towards.
Another U.S General McChrystal said about Karzai,
It was the civilian casualties that drove him crazy. He(Karzai) was
convinced that it would cause us to lose. “You’re creating so much
hate and ill will that we will lose the war,” he told McChrystal.
One other point of discontent was the corruption. In his viewpoint the corruption coming through the international donor contract was much significant. In another interview he said,
I knew that yes, we had corruption in the Afghan government system, in
the delivery of services. But that was, in comparison to the
corruption coming through the international donor contracts, and the
way the money was spent, really insignificant.
There is also some other points. Hamid Karzai is seen inadequately capable to build democratic institutions. He had little experience in politics. One paper noted,
Karzai brought with him to office little experience in governing but
many political habits derived from years of Afghan tribal and war
politics, particularly power balancing rather than institution
building and extreme suspicion about the other side’s motives when he
felt threatened.
Maybe USA(or Holbrooke) wanted someone else who are more malleable to their policy. This can be the motivation to replace him.