Conflicts at work can easily intensify emotions in both parties. For many people, it's very easy to slip up and use attacking words that make the other person feel threatened. For example, an agitated co-worker might say something like, "You always miss important deadlines," or "Is this project too hard for you?"
Obviously, these statements are unlikely to foster a helpful conversational space. Attributing one part of a person's personality or work history to their entire performance is bad professional form and probably says more about you then it does about them.
What's more, overly general, judgmental language immediately puts other people in a defensive mode. And sarcasm just worsens confrontation and breeds resentment that can last far longer than the anger of the immediate conflict.
Instead, stick with objective, professional language. If you feel more agitated during the conversation and feel emotion-laden words welling up, you may need to leave the meeting and return to the topic later.