There are two ways of avoiding things. Actively and passively.
If you see somebody you don't want to meet, and choose to walk in a big circle around them, you are avoiding them actively.
If you had work that should've been done, and you just don't do it, you are avoiding work pasively.
To avoid things is in opposition to the concept of facing your fears. It is seldom looked upon as a wise action, but mostly cowardly, even though it can be wise in a few cases. For instance if avoiding a person makes life better for both of you. Or if you are avoiding danger just because it is incredibly stupid to pursue it.
Avoid is the antonym of pursue.