The first time you meet another person, it is perfectly acceptable to use the standard expression: “How do you do?” Slightly less formal are the alternatives, “Hello, Bob. I’m glad (happy, pleased) to meet you.” In an informal situation, people may also say, “Nice to meet you.” In informal situations, especially young people may simply say, “Hi, Bob!” This is especially common when introducing one person to a large group of people.
Japanese tolerates formulas and repeated expressions, but English prefers variations. This is why when Americans meet one another, the second person tries not to repeat the exact greeting in the same way. If the first speaker says, “How do you do?” then the second speaker will probably use another greeting such as, “it’s a pleasure to meet you, Bob.” If the first person says, “Nice to meet you, Jack,” then Jack would change the intonation and reply, “Nice to meet you, Bill.”
Japanese are usually taught in school that when one person says, “How do you do?” the other person is supposed to always supposed to reply, “How do you do?” At the introductory level of English, perhaps this cannot be avoided, but this is not really how adult Americans respond. Used to using set phrases in their own language, Japanese seem to think that it is acceptable to use the same phrase and never seem to realize that Americans do not do this.
Rather, to a native speaker of English, such repetition of “How do you do?” seems mechanical and slightly insincere. By paying attention to what the other person says and by using another expression, Americans show that they are interested in “give and take” with that person. In contrast, by simply repeating the phrase the person has used, you send the subtle message that you are not really interested in talking with the person.