What does Juliet mean when she says, "A rhyme I learn'd even now / Of one I danc'd withal," which can be paraphrased as, "Just a rhyme I learned from somebody I danced with at the party," in Act 1, Scene 5 of Shakespeare's Romeo and Juliet? Why does she say this?
At the point in the play when Juliet replies to Nurse, saying, "A rhyme I learn'd even now / Of one I danc'd withal," it seems that Juliet is not willing to take Nurse into her confidence concerning Romeo (I.v.152-53). True, after she tells Nurse to find out his name, she next says, "If he be married, / My grave is like to be my wedding bed"; however, judging by the punctuation (--), we may actually be able to interpret that remark as an aside, even without the usual stage direction (143-44). In other words, Juliet did not mean for Nurse to hear those words about her feelings; she was only sending Nurse on an errand to learn Romeo's name. Hence, it seems that we can conclude that when Juliet says her lines about her only love springing "from her only hate," Juliet also does not mean for Nurse to hear her (147). These are private remarks to herself.
At this point, she doesn't know if she can fully trust Nurse with her secret about having fallen in love with the enemy. Editor K. Deighton points out that Juliet is terrified that her nurse will relay Juliet's feelings to her parents (Romeo and Juliet, Shakespeare-online). So she covers up what she says by pretending that it is a common rhyme. Therefore, Juliet said it was a rhyme because (1) she was speaking privately to herself and did not mean for Nurse to overhear, and (2) she's not sure that she can trust Nurse with such a great secret.
The actual wording of the scene described in this question is as follows:
His name is Romeo, and a Montague;
The only son of your great enemy.
My only love sprung from my only hate!
Too early seen unknown, and known too late!
Prodigious birth of love it is to me,
That I must love a loathed enemy.
What's this? what's this?
A rhyme I learn'd even now
Of one I danced withal.
She means that meeting Romeo and falling instantly in love with him created an impossible situation, and one that has a long history in her family. The feud between the Capulets and the Montagues is so ancient and so fraught with prejudice that it's barely even logical, that it has the quality of a fairy tale or even a children's "rhyme" or song, because it's become the stuff of legend even in Juliet's lifetime. The play itself portrays the story of the lovers as another aspect of this mythic history of the two families.