Rashi citing Sanhedrin 36a: (They were judging Naval.) This teaches that in capital cases, we begin with a smaller Chacham. Radak - had David said his opinion first, others would not want to disagree, and would say like him. They concluded that Naval is Mored b'Malchus, for all Yisrael heard that David was anointed to be king. Naval disgraced him and called him a slave!

Radak: Even though David's men could have killed Naval's household without David, amidst great anger also he girded his sword.

Malbim: David considered himself to be king, for a Navi anointed him and most of Yehudah sided with him. Girding his sword showed that he holds that Naval is Chayav Misah for rebelling against Malchus Beis David.