Technically the Undead do not need to breathe, but many do so because it helps with their sense of conversational pacing as technically the Undead do not need their lungs to talk. Which can at times lead them to go a hundred miles a minute in conversations.
Also, many Undead do hold to the habit of breathing out of sheer habit. A lot of intense debates between Undead often arise from one camp feeling they should abandon habits that serve no purpose other than to replicate things they needed to do when they were alive (eat, breathe, sleep) while others maintain a strong desire to keep to those habits because it helps them feel normal.
The habit of breaking into slap-fights during arguments however is one that both sides seem to be ok with upholding…at least if any of those intense debates are anything to go by.