I never really considered myself an extrovert before I realised just how differently different people respond to the idea of being introduced to their friends' friends. Because I absolutely think it's a wonderful idea, if I like both of these people and they both like me, then surely they would love to meet each other, too! What a better gift I could give to a friend, than another friend? And I can give that to two of my friends at the same time!
Then I learned that there are people who absolutely do not like that. It doesn't matter to them who this other person is, adding extraneous new people is not in their budget.
You need to give me more to go on than just "your friend". Introduce us if we have something in common we can both latch onto and use to introduce ourselves to each other, otherwise they're just a stranger im obliged to be pretend to be friendly with and that is draining as hell.
Not to mention the fairly obvious thought that, just because A gets along with B and C does not mean B and C will also get along together.
Friendship isn't transitive, if it was everyone would get along with everyone else.
By all means introduce friends to each other, just don't assume it'll work out, and give them something to work on. Like introducing animals to each other, get them used to each others scent and be prepared to separate them again, you don't just throw them in the same room and hope for the best, then act surprised when they slink off to opposite corners and start growling at each other.
