If your description of the man is true, that he is arrogant, this will be considered
forbidden backbiting. If the man is not arrogant, your description will be a lie and slander. It was authentically narrated on the authority of
Abu Hurayrah (may Allah be pleased with him) that
The Messenger of Allah (peace be upon him) said, "Do you know what backbiting is?" They (the Companions) said, "Allah and His Messenger know best." Thereupon, he (the Prophet) said, "Backbiting implies your talking about your brother in a manner which he does not like." It was said to him, "What is your opinion about this if I actually find (that failing) in my brother what I made a mention of?" He said, "If (that failing) is actually found (in him), you will in fact have backbitten him; if it is not in him, it will be a slander.
May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.