Two management researchers at Louisiana State University reviewed the research on team conflict and came up with some ideas as to how task conflicts turn personal. The connection they found was emotion. Studies and common sense tell you that introducing negative emotions such as anger into a task conflict is going to help things go bad.
The questions then becomes, "How do you prevent those negative emotions from winning out?" These authors proposed some ways. First, teams whose members have greater "emotional intelligence" (EI) will be better able to handle task conflict. EI means being able to recognize and express emotion accurately, understanding emotion, and controlling emotion in yourself and others. An individual with higher EI—and therefore a team with higher collective EI—should be better at coming come up with specific techniques such as controlling both internal emotion and outward displays during task debates.
Strong personal ties between people will help members see emotion in others as a "bad day" or mere frustration with a problem rather than as personal attacks or threats. Those ties also will increase trust, which in turn prevents negative emotion from rising through fear of the other person. Strong ties are built through spending time together, sharing emotions, doing favors for each other and feeling obligated to each other.
Finally, the authors suggested, having strong group norms against negative emotion will help teams resist personal conflict. For example, in one study, top management teams who regularly practiced (had a "norm" for) open exchanges of ideas experienced less relationship conflict. Norms encouraging positive emotion help, too: one study "discovered that humor on the job was common in the teams experiencing low relationship conflict…" Source: Yang, X., and K. Mossholder (04), "Decoupling Task and Relationship Conflict: The Role of Intragroup Emotional Processing," Journal of Organizational Behavior 25:589.