“I hear you say "Why?" Always "Why?" You see things; and you say "Why?" But I dream things that never were; and I say "Why not?"”
The Serpent, in Pt. I : In the Beginning, Act I; this quote is sometimes misattributed to Robert F. Kennedy; it is often paraphrased slightly in a few different ways, including:
You see things as they are and ask, "Why?" I dream things as they never were and ask, "Why not?"
Variant: You see things; and you say "Why?" But I dream things that never were; and I say "Why not?
Source: 1920s, Back to Methuselah (1921)
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George Bernard Shaw 413
Irish playwright 1856–1950Related quotes

“…I always say to people, If you share my dream, why don't we walk together?”
And that's my only organizing tool.
On organizing people to come together in “Meet Pioneer of Gay Rights, Harry Hay” https://progressive.org/magazine/meet-pioneer-gay-rights-harry-hay/ in The Progressive (2016 Aug 9)

Though Kennedy stated that he was quoting George Bernard Shaw when he said this, he is often thought to have originated the expression, which actually paraphrases a line delivered by the Serpent in Shaw's play Back To Methuselah: “You see things; and you say, ‘Why?’ But I dream things that never were; and I say, ‘Why not?’". This phrase was first used by his brother John F. Kennedy in 1963 (June 28th), during his visit to Ireland, in his address to the Irish Dail (Government): "George Bernard Shaw, speaking as an Irishman, summed up an approach to life, 'Other people, he said, see things and say why? But I dream things that never were and I say, why not?" ( Address on YouTube https://www.youtube.com/watch?v=8ADeazX9blw.). Robert's other brother Edward famously quoted it (paraphrasing it even further), to conclude his eulogy to his late brother after his assassination (8 June 1968): Some men see things as they are and say why? I dream things that never were and say why not? - (Eulogy in CBS news video) http://www.cbsnews.com/video/watch/?id=5268061n
Misattributed
Source: Robert Kennedy in His Own Words: The Unpublished Recollections of the Kennedy Years

Speech at Catholic University, Columbus School of Law http://web.archive.org/web/20040704015129/http://www.law.cua.edu/News/Things%20That%20Never%20Were.cfm (2004).
2000s

"Breathe"
2000s, Hotel Paper (2003)
Context: I've been driving for an hour; just talking to the rain. You say I've been driving you crazy, and it's keeping you away. So, just give me one good reason. Tell me why, I should stay. Because I don't want to waste another moment, saying things we never meant to say. And I? Take it, just a little bit. I? Hold my breath and count to ten, I? I've been waiting for a chance, to let you in. If I just, breathe? Let it fill the space between? I'll know, everything is alright. Breathe, every little piece of me. You'll see, everything is alright. If I just, breathe.

Cf. Bernard Shaw, Back to Methuselah (1921), Pt. I : In the Beginning: I hear you say "Why?" Always "Why?" You see things; and you say "Why?" But I dream things that never were; and I say "Why not?"
Books, Brain Droppings (1997)
Variant: Some people dream of things that never were and ask, Why not? Some people have to go to work and don't have time for all that shit.