There are a lot of reasons for this:
Manners are self-reinforcing. In the US, it's generally considered inappropriate / rude / tacky / a bad idea to discuss your income. This is just one of those things that's drilled into you, like chewing with your mouth closed. Even if someone doesn't judge you for your salary, they'll judge you because you're talking about it. Polite people don't do that; where are your manners?
People judge you whether you're rich or poor.
Oh, you're poor? Well, no wonder. You're lazy -- you took off two days last week just 'cause -- and you waste money. I saw you eyeing that purse. Maybe if you stopped spending so much money you'd finally be able to afford it.
Oh, you're rich? No wonder you asked what kind of car I bought. God, you're such a snob, with your fancy car and fancy shoes. And, seriously, what was up with you not just splitting the bill at that restaurant we went to? You make 3x times as much as us, and you didn't want to chip in for the 3 bottles of wine just because you didn't drink? Ugh.
Basically, it's uncomfortable for your friends to see you as rich or as poor. So why give them that information?
Money differences create distance.
Most of your friends don't make as much money as you. They might make more, and they might make less. But they probably don't make the exact same. So whatever your salary is, you're now setting yourself apart as different.
People equate salary with richness.
High salary? People will see this as your not having to save like they do. They may not realize that you have a sick parent to take care of and you aren't really all that rich.
Low salary? People might wonder why you're not saving more -- you have your kid's education to think about! What were you thinking buying that house? Of course, they don't realize that you inherited that house from your grandmother.
Bragging is bad.
If someone volunteers that they went to Harvard, people are very quick to perceive this as "bragging," even when it was completely relevant to the conversation. So, Harvard alums will often just say they went to school in Boston. There are some things that are seen as so inherently elitist that simply saying them gets your action classified as bragging. High incomes are one of those things. The saying-my-salary-is-bragging feeling is so ingrained that it's there even when people directly ask. Bragging is considered bad in the US because arrogance is bad, as it being mean or insensitive to others.
It makes other people uncomfortable.
Even if you don't judge people on salary, and you don't think your friends will judge you based on your salary, it still might make them feel bad about themselves (if you're out-earning them). High incomes are seen as a sign of success. If you're out-earning your friends, they might feel bad that they aren't successful enough.
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Manners are self-reinforcing. In the US, it's generally considered inappropriate / rude / tacky / a bad idea to discuss your income. This is just one of those things that's drilled into you, like chewing with your mouth closed. Even if someone doesn't judge you for your salary, they'll judge you because you're talking about it. Polite people don't do that; where are your manners?
People judge you whether you're rich or poor.
Oh, you're poor? Well, no wonder. You're lazy -- you took off two days last week just 'cause -- and you waste money. I saw you eyeing that purse. Maybe if you stopped spending so much money you'd finally be able to afford it.
Oh, you're rich? No wonder you asked what kind of car I bought. God, you're such a snob, with your fancy car and fancy shoes. And, seriously, what was up with you not just splitting the bill at that restaurant we went to? You make 3x times as much as us, and you didn't want to chip in for the 3 bottles of wine just because you didn't drink? Ugh.
Basically, it's uncomfortable for your friends to see you as rich or as poor. So why give them that information?
Money differences create distance.
Most of your friends don't make as much money as you. They might make more, and they might make less. But they probably don't make the exact same. So whatever your salary is, you're now setting yourself apart as different.
People equate salary with richness.
High salary? People will see this as your not having to save like they do. They may not realize that you have a sick parent to take care of and you aren't really all that rich.
Low salary? People might wonder why you're not saving more -- you have your kid's education to think about! What were you thinking buying that house? Of course, they don't realize that you inherited that house from your grandmother.
Bragging is bad.
If someone volunteers that they went to Harvard, people are very quick to perceive this as "bragging," even when it was completely relevant to the conversation. So, Harvard alums will often just say they went to school in Boston. There are some things that are seen as so inherently elitist that simply saying them gets your action classified as bragging. High incomes are one of those things. The saying-my-salary-is-bragging feeling is so ingrained that it's there even when people directly ask. Bragging is considered bad in the US because arrogance is bad, as it being mean or insensitive to others.
It makes other people uncomfortable.
Even if you don't judge people on salary, and you don't think your friends will judge you based on your salary, it still might make them feel bad about themselves (if you're out-earning them). High incomes are seen as a sign of success. If you're out-earning your friends, they might feel bad that they aren't successful enough.

Why is it considered extremely rude to inquire about other people's salaries and income in the US?
Answer (1 of 46): I'd say it's rude because it has the ability to strike a nerve. It's kind of like asking a person why they haven't had kids yet. Maybe they haven't tried, or maybe they've been trying for a long time and haven't had any luck. Asking such a question can invoke embarrassment, sham...