The antonyms for the word "meeting privately" can vary depending on the context. In a professional context, the opposite of a private meeting could be a public meeting, a conference, or an open discussion. In a personal context, the opposite of a private meeting could be a social gathering, a party, or a large event. In some cases, the antonym for a private meeting could simply be a casual conversation, a chance encounter, or an impromptu meeting. It all depends on the circumstances surrounding the meeting and the level of formality or intimacy desired.