Final answer:
The behavior being exhibited is called denial, which is a defense mechanism where individuals refuse to acknowledge the existence of a problem or conflict in order to avoid discomfort and consequences.
Step-by-step explanation:
The behavior being exhibited by a person who refuses to face up to a conflict either by giving in or by pretending nothing is wrong is called denial. Denial is a defense mechanism where individuals refuse to acknowledge the existence of a problem or conflict in order to avoid the discomfort and potential consequences that come with facing it.