Quite often (9 out of 10 times?), on radio (NPR), when the interviewer says "Thank you" to the interviewee, the reply is also "Thank you."
What has happened to "You're welcome?" Why is "You're welcome" so uncomfortable to say?
You have it wrong. Nothing has happened to "you're welcome."
While it is certainly reasonable for the interviewer to thank the interviewe, it is not unreasonable for the interviewee to appreciate the opportunity to speak. The interviewee's thank yous should be interpreted as "no, thank you [for letting me speak]," rather than as 'you're welcome."
You guys are making it too complicated. I give you a simple example happening in our daily life. When you are looking for a job, at the end of the interview, the interviewer usually ends it up by saying "Thank you for your time." You wouldn't response "you are welcome" because you are clear that you are both doing each other a favor, instead of only you're doing the favors. So you probably want to say "Thank you for giving me a chance" to acknowledge his effort, too, as a human being with the basic manner. So it's the same scenario in air shows that the host and the guest are actually doing each other the favors, so they should be both thankful to each other.
As Fengyang Wang commented on another answer, "You're welcome" runs the risk of sounding arrogant and implying that the thanks given was expected or deserved. For this reason I don't use it often, and I usually advise English learners not to use it unless they're really comfortable with its usage. There are much clearer and more meaningful/creative ways of responding to thanks such as:
that both avoid this risk and avoid sounding canned and insincere.
Nice observation. I think it really depends on "the company." If the two are somewhat "familiar" with each other perhaps "Thank you" could be more appropriate. But when the two are on less familiar terms, "You're welcome" is common. If it's radio, it could also be that the two are mutually thankful for each other.
Your question is a good one, and I recommend taking a look at Harvey Sacks (1994) "Conversation Analysis." Observations like yours are in the book and answers like mine are in there as well.
Notice, as above, when asking directions in a "foreign place," you will hear "You're welcome" more (Sacks, 1994) because the folks "want to be polite" with you.
While I completely agree with everyone else who has answered that in the context mentioned in the question, both parties are doing a favour to each other and hence they both thank each other, I feel that at least for certain speakers of the language, '"you're welcome" is beginning to sound arrogant. I am aware that many people disagree with this opinion but this answer does not reflect the views of the entire English I speaking community. As mentioned in the comments above, a lot of people (especially of the younger generations) feel that "you're welcome" is becoming a phrase that contains hints of arrogance as if the person saying it is saying that he is DESERVING of thanks. At least with most of the speakers with whom I communicate, we tend to use phrases such as 'no worries' and 'no problems' instead of thanks, which express the sentiment that we are glad to be of service to whoever is saying 'thanks'. While "you're welcome' used to convey this sentiment some years ago, in my opinion it doesn't do so today. Maybe this can be attributed to the fact that the younger generation tends to use this phrase sarcastically. As some have pointed out, tone is of utmost importance when using this phrase as one can easily offend someone using a harsh tone.
"You're welcome" has not lost its meaning and won't sound arrogant either, if done graciously.
See this conversation:
Person1: "Thank you very much for taking the time"
Person2: (smiling graciously) "You're most welcome. Thank you too for giving me the opportunity"
Person1: (smiling) "My pleasure"
Perhaps the other reason people don't say "You're welcome" is a "monkey-see-monkey-do" of observing others not saying it, and thinking that it's the right way of responding. For others, it just may be a way of making the conversation quicker (although I do agree that people might feel worried that it might sound arrogant).