When Juliet says 'that I must love a loathed enemy' she and Shakespeare are telling us a lot about prejudice, bigotry and blind hatred both in the play 'Romeo and Juliet' and in the world in general through the ages of history. For example, Juliet does not loathe Romeo's family - she has never even met them as far as we are told in the play. Living in old times when aristocratic girls were very protected and shelterd, it is unlikely that she has even been witness to the petty street fighting and brawls - though she may have heard about them. So she has no reason to personally hate the family. The dangerous thing about hate is when it is inherited mindlessly and needlessly and the pain and trouble it causes - as mentioned by the Prince who is worried where it will all lead.
Not surprisingly, they are both pretty shocked and unhappy. It would be strange if they did not react like that. After all, it's not every day that you fall in love and find out your family is having a blood feud with the family of the person you love.
Juliet says that love is a monster for doing this. She says that she found out too late who Romeo was and now it is too late.
Romeo says that he is in deep trouble now because his life is in the hands of his enemies, the Capulets.
Each character uses a metaphor.
Is she a Capulet?
O dear account! my life is my foe's debt.
Ay, so I fear; the more is my unrest.
Here we watched Romeo refer to the news through a financial metaphor as if he knows this isn't going to work out, in fact he'll end up owing something.
Go ask his name: if he be married.
My grave is like to be my wedding bed.
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.
Juliet's metaphor likens her wedding day to a grave. She'd rather die than be with anyone other than Romeo.
I think the response from both of them shows dramatic emotion and demonstrates they both hoped for something that would succeed.