BRABANTIO
This is Venice. My house is not a grange.
[…]
IAGO
Because we come to
do you service and you think we are ruffians, you'll
have your daughter covered with a Barbary horse,
you'll have your nephews neigh to you, you'll have
coursers for cousins and jennets for germans.
[…]
I am one, sir, that comes to tell you your daughter
and the Moor are now making the beast with
two backs. (1.1.119; 123-127; 129-131)
We've seen how Iago uses animal imagery in his racist diatribe against Othello, which is grounded in the idea that black men (and women) are inhuman. Here, Brabantio objects to Iago's middle-of-the-night assertions that Desdemona has eloped by saying his house isn't a "grange" (a farm or a farmhouse). Iago takes the opportunity to pun on the term "grange," as he claims that Desdemona is having sex with a "barbary horse" and, as a result, Brabantio will have relatives that "neigh to him." Desdemona and Othello, he says, are "making the beast with two backs" (in other words, humping, like camels). This isn't the first time Iago has implied that Othello's animal-like sexuality corrupts Desdemona. Compare this to 1.1.106-113 above.
Quote 2
BRABANTIO
She, in spite of nature,
Of years, of country, credit, every thing,
To fall in love with what she feared to look on!
It is a judgment maimed and most imperfect
That will confess perfection so could err
Against all rules of nature, (1.3.114-119)
Desdemona's father argues that her love for Othello is unnatural, since, according to him, Desdemona would never fall for a black man who she "fear'd to look on." Of course, Brabantio couldn't be more wrong about his daughter – Desdemona is in love Othello. It seems that Iago has played Brabantio perfectly. Iago knew that Brabantio was racist and, as previous passages demonstrate, he used Brabantio's attitude toward the idea of a mixed marriage in order to rile the man against Othello. Brabantio repeatedly insists that Othello must have "enchanted" Desdemona with "foul charms" and magic spells. Otherwise, he insists, Desdemona never would never have run "to the sooty bosom" of Othello (1.2.70).
Quote 3
BRABANTIO
Look to her, Moor, if thou hast eyes to see.
She has deceived her father, and may thee. (1.3.333-334)
Brabantio perpetuates a pretty unfair stereotype of young women in these lines – he suggests that since Desdemona has "deceived her father" by running off to elope with Othello, she'll probably "deceive" her new husband too. The idea is that an unruly daughter will make an unruly and promiscuous wife. Compare this to 3.3.17, below.