I'm'a let you finish, but...
One of my pet peeves in being interrupted by the person I'm talking to. I know I do it myself, too, sometimes, though, so I'll confess to a minor hypocrisy there.
One of my pet peeves of greatest egregiousness, though, is being interrupted by someone else who wasn't ever part of the conversation (and wasn't invited in). Now to clarify: it's not that they're interrupting for the sake of contributing something into the conversation (a fact-correction, or a jog-your-memory when you're struggling to think of a movie title, for example; those interruptions I will oftentimes value). I'm talking about, just to use an example from this past Sunday, when I'm listening to a story from a friend after church and a stranger-to-me comes up, interjects him/herself into our conversation, and begins talking to my friend about a completely different topic, cutting off my conversation and excluding me.
If you pay attention, you'll start seeing people do this all. the. time. At church, at work, at weddings, in the lunchroom, basically anywhere and everywhere social. It irks me when I see it happen to others, and drives me nuts when it happens to me.
When did this behavior become an acceptable social norm?
I've struggled for years about what to do in this situation. On the rarer occasion I'm the person who the newcomer is engaging, rather than being the odd-man out, then I tell them, hang on, I was just talking with so-and-so, let me finish that conversation up first (or, if the newcomer brings urgent news that must be addressed immediately, then I'll apologize to my first friend, and promise to follow-up with them later; this is less preferable, but sometimes necessary).
But most of the time I'm the one not being approached, which typically leaves me standing by uncomfortably until the 3rd party finishes and walks away, allowing person #1 and I to resume. By then I've wasted 5 minutes waiting (and awkwardly eavesdropping) on another conversation to resolve in order to continue the conversation I was already having. Frankly, I'm sick of this solution.
From now on, I think I'll try implementing some new approaches:
1) Walking away. Clearly, if my friend thinks the newcomer's conversation is more interesting than the one we were having, well, then sadly the odds are they were already disengaged from our conversation anyway.
2) That solution won't work all of the time, though, because sometimes I still need information from the friend I was talking to. In that case, I need to work on a polite and direct way of asking the newcomer, "may we finish our conversation first, or is this urgent?" Actually, that right there might do it...
People checking their phones in the middle of a conversation is also a pet peeve, but I've probably ranted enough for one evening.