Why at the moment we greet somebody for the first time we say?:
How do you do?
And the another person replies:
How do you do?
Why at the moment we greet somebody for the first time we say?:
How do you do?
And the another person replies:
How do you do?
"How do you do?" is technically a question, but really, it's just an expression. One person says, "How do you do?", and the other person does not answer, because no answer is needed.
If you prefer, you can answer, but you have to say, "Very well, thank you, and you?". You aren't allowed to launch into an explanation of exactly how well you are or are not doing and why.
This is less about English as a language than manners in the English-speaking world.
"How do you do?" a formal greeting for someone that you have not met before. It's not a question but a fixed expression. It was once commonplace, especially among the English upper classes. It's not a question asking about someone's health.
If somebody says "How do you do?" to you, the polite way to reply is "How do you do?". It is not meant as a question and an answer is not expected.
Oscar Wilde's Lady Windermere's Fan, 1892
This is traditionally British formal English. Stilted and old-fashioned nowadays.
Sometimes people reply with "Hello" or "Pleased to meet you".
Interesting notes:
In the 16-18 centuries there was a phrase in use "How do you?" that is an equivalent of our present day "How are you?".
An old-fashioned phrase "How do you do" means "a difficult, worrying, and unpleasant situation"