WordNet sense 1 (inclined or showing an inclination to dispute or disagree, even to engage in law suits):

contentious, disputatious, litigious, disputative

WordNet sense 2 (striving to overcome in argument):

agonistic, agonistical

WordNet sense 3 (involving competition or competitiveness):

competitory

WordNet sense 4 (having or showing a ready disposition to fight):

bellicose, battleful