Here’s a response I’ve seen about this around the net for a while now that feels right.
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"Actually, the “you’re welcome/no problem” issue is simply a linguistics misunderstanding. Older ppl tend to say “you’re welcome,” younger ppl tend to say “no problem.” This is because for older people the act of helping or assisting someone is seen as a task that is not expected of them, but is them doing extra, so it’s them saying, ‘I accept your thanks because I know I deserve it.”
“No problem, however, is used because younger people feel not only that helping or assisting someone is a given and expected but also that it should be stressed that your need for help was no burden to them (even if it was).”
“Basically, older people think help is a gift you give, younger people think help is a requirement.”