3.1 First principles. For Descartes, it was "I think, therefore I am." That is OK as far as it goes, but it only goes so far, because people do a lot more than think. I'd go further: I feel, therefore I am; I see, therefore I am; I dream and create, therefore I am; I am hungry, therefore I am; I hurt, therefore I am.
3.2 "Hurt" by Trent Reznor (Nine Inch Nails)
I hurt myself today
To see if I still feel
I focus on the pain
The only thing that's real
3.3 What do humans exist "for"? We exist for our genes; our bodies are survival machines built by our genes for the purpose of making more copies of themselves. Our thirst for life, our drive to survive, all of our pain and all of our striving to avoid pain -- these things are all "for" our genes. We suffer existence because of the biological imperative of replication. (See Richard Dawkins, The Selfish Gene and The God Delusion.)
3.4 So: I hurt, therefore I am. There's something fundamental, something primal, about the way our entire lives are spent scratching one itch after another. This is also the Buddhist "All existence is suffering."