Interrupting a Monologue to Have a Conversation

In the past week, when I've interjected something in a friend's narrative when I thought we were having a conversation, I've seen that the person wanted to finish her monologue before having any input from me.  This happened with both a friend and a relative.  (I'm not implying that relatives can't be  friends.)

I've been guilty of high-jacking a bit of conversation and taking it off into an unplanned area against the pilot's wishes, but this wasn't one of those times. 

In both cases, I was trying to interject something that I thought would really help the other person.  I thought my interjection should that I was being attentive and concerned.  

But who knows?  Maybe if I had a recording of the conversation, I'd hear things differently.  

More on this tomorrow.