Shylock's two most important quotes relate to his position as a social outsider. Though ruthless in his aims to destroy Antonio, Shylock gains some measure of sympathy from the audience (particularly modern audiences) through the antisemitism he faces from others. He has reasons for feeling justified in his desire for revenge.
The audience first learns of Antonio's hatred for Antonio in act 1, scene 3. While talking with Bassanio about arranging a loan for Antonio, Shylock tries to stay all business, though he harshly rebuffs Bassanio's dinner invitation. Right as Antonio appears onstage, Shylock delivers this sour aside to the audience:
How like a fawning publican he looks!
I hate him for he is a Christian,
But more for that in low simplicity
He lends out money gratis and brings down
The rate of usance here with us in Venice.
If I can catch him once upon the hip,
I will feed fat the ancient grudge I bear him.
He hates our sacred nation, and he rails,
Even there where merchants most do congregate,
On me, my bargains and my well-won thrift,
Which he calls interest. Cursed be my tribe,
If I forgive him!
Before this scene, the audience might have wholly sympathized with the melancholy Antonio. However, Shylock is giving them an alternate look at the character: Antonio, so loyal to his friends, is also capable of bigotry and cruelty. The term "publican" evokes two-faced politicians, who present a virtuous facade to the world while hiding the corruption beneath.
The following from act 3, Sscene 1 is perhaps Shylock's most famous speech in the play, which he delivers to the mocking Salarino and Solanio as they argue against his taking a pound of Antonio's flesh for vengeance, asking him what he could possibly do with it:
To bait fish withal: if it will feed nothing else,
it will feed my revenge. He hath disgraced me, and
hindered me half a million; laughed at my losses, mocked at my gains, scorned my nation, thwarted my bargains, cooled my friends, heated mine enemies; and what's his reason? I am a Jew. Hath not a Jew eyes? hath not a Jew hands, organs,
dimensions, senses, affections, passions? fed with
the same food, hurt with the same weapons, subject
to the same diseases, healed by the same means,
warmed and cooled by the same winter and summer, as
a Christian is? If you prick us, do we not bleed?
if you tickle us, do we not laugh? if you poison
us, do we not die? and if you wrong us, shall we not
revenge? If we are like you in the rest, we will
resemble you in that. If a Jew wrong a Christian,
what is his humility? Revenge. If a Christian
wrong a Jew, what should his sufferance be by
Christian example? Why, revenge. The villany you
teach me, I will execute, and it shall go hard but I
will better the instruction.
Here, Shylock is vengeful and bitter. Building upon the previous speech where he establishes his reasons for hating Antonio, here he elaborates on why he despises Christians in general. He has been abused and mistreated, so he argues it is only human that he respond in kind. He appeals to a shared sense of humanity between himself and Christians, not to create reconciliation between them, but to make clear that he is not indulging in such grotesque demands just because he is bloodthirsty—he wants to return the pain he's endured in kind. It's all about the intersection between pain and revenge, and those are Shylock's defining traits.