The phrase "were on one case" suggests teamwork and collaboration towards a specific goal. Antonyms for this phrase can be words and phrases that indicate disunity or lack of coordination, such as "working independently," "disconnected," or "out of sync." These words imply that individuals or groups are not working together to achieve a common objective, and the result may be disjointed or ineffective. "Not on the same page" or "divergent" are also potential antonyms for "were on one case," as they suggest a lack of shared understanding or agreement. However, it's important to remember that effective communication and collaboration are essential for achieving success in any endeavor, be it professional or personal.