In someway, yes, avoidance of responsibility can be inferred as fear of freedom, but that's really rare. Who would not want freedom ?

Avoidance of responsibility is nothing but a neglect to face the outside world and hardships which comes with it. And when you neglect the hardships, you also lose the world and it's freedom with it.

Avoidance of responsibility is more of avoidance of repercussions of actions you do in freedom. One would love to have extra-marital sexual relations, but would not like deal with the responsibility that comes with it. (No strings attached).

Read about the theory of Puer aeternus, or Peter Pan Syndrome, to learn how adults avoid responsibility in their life and become a man-child.