You seem extremely confused. I said that generals have no authority such that soldiers must listen to them over the POTUS. I also said that they swear an oath to the Constitution and to no officer.

The authority of the C-in-C is considered supreme and ultimate but without military rank, in that it cannot be gainsaid by subordinate officers while also maintaining civilian status. These are Constitutional and legal terms of long, long history. You should look them up.

This authority is by no means considered unilateral, which is the word you're groping for. It can, and has, been gainsaid by other members of the Executive Branch, who share in that authority, and Congress may also limit the authority through its sole power to declare war and its ability to restrict both war funding and deployments longer than 60 days.