First of all, there is no such practice in the Bible. The only excuse they would use is that John or Andrew also "introduced" Jesus to others, which has nothing to do with introducing a friend for John the Baptist was acting as the herald of Christ. Andrew was proclaiming a good news.
Today, it is a common habit in companies to introduce one worker to another, one associate to another. Many churches pick up on this because they do not have true fellowship of the saints. It seems nice. Yes, I would use only the word "nice" - from the Latin meaning foolish. This practice, I believe comes from the ancient way of heralding the coming of a great one. However, to herald a great one to a friend today, is rather rare. And to say that a common worker or friend is worthy to be "heralded", is virtually hypocritical, for there is usually no such respect.
Now this is not the same as introducing others who are in need to someone who has the help to offer.
Conclusion, if we are to "introduce" someone, keep in mind that we are heralding him or her, and we better mean it or we don't do it all together. Because when we herald someone, he or she rightly deserves such greatness and therefore we do not deserve any gratitude. It would take tremendous hubris to have to slightest expectation of gratitude for introducing one to another, regardless of who the "introducer" is. In fact, we should be grateful ourselves for being allowed the opportunity to herald a great person. I will not expound on the definition of greatness here, I will only say that "great" here doesn't necessary refer to someone of high ranking of sorts. If we "herald" (yes it must be herald for there's no such thing as "introduce" in this context) the wrong person to someone, it is our responsibility to bear the guilt and embarrassment. As for those who have no shame from this vanity and mistake, I don't know how they differ from beasts.