People with competing conflict styles are assertive and uncooperative. They are able to advocate for their own needs and coerce action from others. They seek control over a conversation in both the substance of the argument and the ground rules over which the argument is had.
Because a competing conflict style is based on the premise of winning, there will ultimately be a loser.
A competing conflict style can be useful in certain circumstances where winning is the goal, such as dealing with an equally aggressive external party with whom you don't need to build an ongoing relationship. However, in personal matters with loved ones, friends, or even coworkers, a competing conflict style can sour long term relationships. In these circumstances, people with a natural instinct for a competing conflict style would be wise to think less about winning and optimizing for their own short-term needs and channel that mindset into how they can create create wins for the people they rely on and care about. Sacrificing wins in the short term will create more wins in the long term.