Hadith: If you are three, then two should not converse privately with the exclusion of the third, until more people join you, because that would grieve him

عن عبد الله بن مسعود رضي الله عنه قال: قال رسول الله صلى الله عليه وسلم : "إذا كنتم ثلاثة فلا يتناجى اثنان دون الآخَر، حتى تختلطوا بالناس؛ من أجل أن ذلك يحُزنه".
[صحيح] - [متفق عليه]

ِ‘Abdullāh ibn Mas‘ūd (may Allah be pleased with him) reported that the Prophet (may Allah's peace and blessings be upon him) said: "If you are three, then two should not converse privately with the exclusion of the third, until more people join you, because that would grieve him."
[Authentic hadith] - [Narrated by Bukhari & Muslim]

Explanation

Islam encourages empathy as well as good manners and speech in all gatherings. Islam also forbids everything which may harm, frighten, or cause negative or evil thoughts. Two people privately conversing in the presence of a third hurts the feelings of the third person and makes him feel sad and undeserving of taking part in their conversation. It also makes him feel ignored and left out. Hence, Islam forbids this kind of private conversation.