Cooping up refers to the act of restricting or confining someone or something. The antonyms for cooping up are releasing, freeing, liberating, and setting free. Releasing means to allow someone or something to go free, while freeing implies the act of setting someone or something free from bondage. Liberating means to grant freedom and independence to someone or something. Finally, setting free means to release or untie something from confinement. By using these antonyms, one can express the opposite effect of cooping up, which is to grant freedom, independence, and room for movement.