It's in keeping with US views on exceptionalism. I don't think the USA has any particular problem with the convention (nothing that couldn't be resolved by signing it with specified reservations, as some other nations). Rather the problem is with the concept of something which is universal.
The key problem is that the USA is the only democratic nation that persists in the assertion that its law is supreme. On matters of human rights all nations should be subject to the international community. With all sorts of limits and reservations all are, save the USA. The key problem for the USA is that it has in many states a policy of judicial murder of criminals (the death penalty) which it keeps precisely because it does not agree the international consensus that the state must not murder.