In Act I of Romeo and Juliet, why is Romeo so unhappy?

Romeo is unhappy because the girl he is in love with doesn't return that affection. After the street fight in Act I, Scene 1, Lord Montague, Romeo's father, comments that his son seems sad and depressed. He asks Benvolio to discover Romeo's problem. Romeo tells Benvolio that his days are long because he is "Out of her favor where I am in love." He is seemingly confused and frustrated by this unrequited love and launches into a series of oxymorons describing his plight: "O brawling love, O loving hate." He further explains that the girl he loves basically refuses to love and has chosen to live "chaste." He compares her to the Greek goddess Diana, who was the patroness of virginity. She refuses to be talked to about love or take gifts. She is very beautiful but won't share her beauty. Romeo says,

Well in that hit you miss. She’ll not be hit
With Cupid’s arrow. She hath Dian’s wit,
And, in strong proof of chastity well armed,
From love’s weak childish bow she lives uncharmed.
She will not stay the siege of loving terms,
Nor bide th’ encounter of assailing eyes,
Nor ope her lap to saint-seducing gold.
O, she is rich in beauty, only poor
That, when she dies, with beauty dies her store.

The audience doesn't learn who the girl is until Romeo reads the list of those invited to Capulet's party in Scene 2 and sees Rosaline's name. Benvolio urges Romeo to go to the party and compare Rosaline to the other women of Verona. Benvolio is sure Romeo will see someone more beautiful. Of course, Benvolio is correct as Romeo meets Juliet at the party.