What makes Frederic Henry a dynamic character is that, over the course of the novel, he lives and learns, changes and grows until, at long last, he achieves the kind of maturity previously only displayed by Catherine. Initially, Henry's a thoroughgoing cynic, who deals with his numerous demons by plunging himself into a life of self-indulgent dissipation. Henry hates the world around him, but instead of trying to deal with his alienation in a responsible manner, he chooses to blot it out through alcohol and meaningless relationships.
This attitude can be seen in Henry's stubborn refusal to face up to the realities of war. The only way he can deal with the conflict is by dropping the subject altogether and pretending that the whole thing's not really happening. Thanks to Catherine, however, he comes to realize that he cannot avoid war any more than he can avoid life. He must participate in the world around him instead of constantly running away from it.
Catherine has shown him how to do that, through believing in something, whether it's love, religion, or country. By the end of the novel Henry's been saved from nihilistic despair to the extent that he experiences a hitherto unthinkable degree of inner peace and security. In other words, he's become more like Catherine, ennobled and transformed by her love.