“What is a poet? An unhappy man who hides deep anguish in his heart, but whose lips are so formed that when the sigh and cry pass through them, it sounds like lovely music.... And people flock around the poet and say: 'Sing again soon' - that is, 'May new sufferings torment your soul but your lips be fashioned as before, for the cry would only frighten us, but the music, that is blissful.” -- Soren Kierkegaard, Either/Or
Every day I remind people that a poem is not a diary, that you cannot make the assumption that the events in a poem have actually happened to the poet even if it has been written from the first person perspective.
Nonetheless, the emotions and insights contained within a poem DO come from the poet, whether or not the experience itself is fictitious. Sometimes these feelings are many years behind us, but like good artists, we never discard anything that might be useful later on... and in that, we are not special. The only difference between a poet (or an artist in any other medium) and someone who doesn't consciously make art is that we are lucky enough to be able to express ourselves in a way that others can understand.
Just think how many people there must be in the world who have their experiences buried deep within them, with no voice to tell us how they suffer. This is why we write: so that they know they are not forgotten.