The antonyms for "most openly" could be "secretively," "discreetly," "furtively," or "covertly." Whereas "most openly" means to do something in a transparent and straightforward manner, these antonyms suggest doing things in a hidden or sneaky way. For instance, when a person is trying to keep a secret, they would act covertly or furtively, which means they are not open about their actions. In contrast, when someone is sharing information without any hesitation, they are doing so in the most openly manner. Understanding these antonyms can help us to precisely describe the way someone is acting or behaving, which is essential in different situations.