In The Catcher in the Rye, how do Stradlater and Mr. Antolini demonstrate falsehood and hypocrisy?

One major theme of The Catcher in the Rye is "phoniness." This is shorthand for the fact that people will let you down. Sometimes it's because of character flaws such as hypocrisy; other times it's simply because of their human weaknesses and limitations.

Stradlater (chapters 3 - 6) is Holden's roommate at school. He is handsome, confident,  arrogant, and selfish. He is also careless. For example, though he takes a lot of care with his appearance -- shaving, combing his hair -- Holden notices that Stradlater almost never replaces his razor. If Stradlater wants to do something (such as borrow Holden's hound's-tooth jacket), all he cares about is that he gets what he wants. He will not be deterred by noticing that he might do some damage in the process (such as stretching out the jacket with his broad shoulders).

Stradlater's selfishness and sense of entitlement make him careless about things like following the rules and noticing people's feelings. For example, he asks (almost demands) that Holden write a descriptive essay for him. (Stradlater is willing to be dishonest.) Holden writes the essay not about a place (which was the assignment), but about a baseball glove that belonged to his brother, Allie, who died of leukemia. Stradlater comes back, glances at the essay, and rejects it out of hand because it's not about a place. He completely misses that it is a very emotional topic for Holden and also (probably) a beautiful piece of writing which might still have gotten a good grade though it did not exactly fulfill the assignment.

Stradlater is not the sort of person we think of when we imagine a hypocrite. He does not spend a lot of time trying to keep up moral or socially appropriate appearances. But that is only because he is clueless and unaware of his own flaws.

We meet Mr. Antolini much later in the book (chapter 24). He is a former teacher of Holden's. Holden calls him up in the middle of the night and asks to come over. Mr. Antolini, apparently recognizing this as a cry for help, agrees.

At first, Mr. Antolini seems like a much better person than Stradlater. Holden has already told us that Mr. Antolini was the one who picked up the body of James Castle, the student who died at Holden's old school, and carried it to the infirmary. Mr Antolini is also intellectual, which Holden values. He listens to Holden more carefully than anyone yet has, and offers some earnest and insightful advice. It looks like Holden has finally found an adult who will be able to help him, and also a place to crash and get some much-needed sleep.

However, right from when Holden arrives, we also get signals that some things are not right in the Antolini household. The Antolinis have just had a party, and Mr. Antolini appears wearing his bathrobe, slightly drunk ("oiled up," as Holden says). Mrs. Antolini is also in a bathrobe, but this is because, we are told, she just got out of bed. We are not told the same thing about Mr. Antolini.

Mrs. Antolini is much older than her husband. There is nothing inherently wrong in this, but it does suggest something might be odd about their marriage.

After getting settled on the Antolinis' couch and finally going to sleep, Holden has an experience that scares him. He wakes up to find Mr. Antolini sitting beside him in the dark, "sort of petting me or patting me on the goddamn head."

Holden is alarmed and disgusted by this. He thinks Mr. Antolini was coming on to him, or trying to molest him in his sleep. (Holden tells us that he has had many experiences like this before, and he "can't stand it.") He makes an excuse and quickly leaves the house, though Mr. Antolini urges him to stay.

It is not entirely clear whether Mr. Antolini was really coming on to Holden. It is possible that in his drunken state he was feeling protective or affectionate toward Holden, as toward a son or younger brother, but patting his head would still be an odd thing to do. It crosses some boundaries, and Mr. Antolini's response when Holden confronted him ("I'm simply sitting here, admiring--") is also suspicious.

But whether Mr. Antolini was patting Holden's head out of open lust, unconscious desire, or simply an ill-judged display of affection, it does seem that at the very least, he was meeting some emotional need of his own in a way that is not appropriate between teacher and student. And whether or not Mr. Antolini intended the gesture as a come-on, it still came across to Holden as a shocking betrayal.