Malbim: Yo'av already knew that David will be upset about his son, like he told Achima'atz (18:20). However, he thought that he will be sad, like the nature of a father, but he will not mourn, for he was killed according to law. We do not mourn over people that Beis Din executes. Yo'av was upset to hear that David mourns, i.e. he thinks that he was killed not according to law, i.e. Yo'av killed him improperly.