The Pentagon is busy covering up it's own war crimes and doesn't want to be accountable for to do so would make U.S. leaders subject to prosecution by this special international court. Clinton doesn't always appear to go along with the Pentagon, but this decision may come from even higher up. The CFR, of which Clinton and Kissinger are members couldn't have wanted this to happen. So, the U.S. is not happy. Israel is not happy.
Many Arab countries are unhappy.
They can simply declare they do not accept the ICC's jurisdiction - if the crime is committed on their territory or by one of their nationals. This is a serious flaw in the treaty. The time frame for establishing the treaty also permits current atrocities to go unpunished. Crimes can continue unabated until the treaty becomes law. And, under pressure from the Arab states, chemical and biological weapons were not mentioned in the final treaty.