Mmm. Is it even worth bothering asking why? Why should they oppose this?
The CSM itself gives us the reason in the subtitle: "because it could impact US military operations abroad".
In other words, aggression defines 'US military operations abroad', therefore it must be opposed.
However, we find there's nothing to worry about, according to State Department legal adviser Harold Koh, because "the US successfully negotiated the “aggression” statute’s wording so that US forces won’t be susceptible to it. “No US national can be prosecuted for ‘aggression’ while the US is not a signatory” to the ICC".
Phew! That's OK then.
They can carry on making aggressive wars to their hearts content...