hmm, I'm not good at critiquing. I read the poem and I can only suggest editing some portions to make it sound smoother. There are words like "the" that are fillers.
"Sometimes, she sees herself flying once again
until the reality wakes her up;"
^ In this case, I consider the word "the" a filler. It sounds good to just say, " until reality wakes her up."
The same for
"and now she is allowed to live
all those wildest desires of her
only in the dreams."
^ The "the" in the dreams is not needed in my opinion.
Also, I feel like the transition between the why she sings and your question of why a caged bird sings, don't quiet come together. I feel that it can be reworded so that the "ah moment" hits the reader without you having to say it. How to do that?
uhmmm... you'll have to play around with it until you feel it.
Other than that, I enjoy the comparison of the caged bird to the lady. Though, whenever I think of a caged bird, I think the bird has been put in that cage without consent. Where as the lady caged herself own her on accord. So due to that the realization you had, of why the caged bird sings, doesn't fully hit home to me in the cased of the lady. Just some thoughts. Sorry, for the rushed comment.