Agonistic is an adjective that means argumentative. Your agonistic attitude might get you in trouble if you're constantly telling people they're wrong.
The ancient Olympics were actually called agones, which meant a struggle to achieve glory. So today, agonistic also refers to anything related to these ancient Greek athletic competitions. The marathon, for example, was an early agonistic event. Don't confuse agonistic with the similarly spelled "agnostic," a person who believes it's impossible to know whether or not God exists. However, if you get into a religious argument with an agnostic, you might find them to be very agonistic.