DEAR MISS MANNERS: I encounter two distinct types of conversationalists, and they tend to form groups in which everyone seems happy with their own style.
The first group is the one to which I belong. We start conversations, after "Hello," by asking a question of the other person. This question might be, "How are you?", "How is your family?" or "How was that movie you went to see?"
The person answers, and then asks the first asker a similar (but not identical) question. Sometimes, someone mentions an experience or piece of news without being asked, but more than half of new topics are introduced by someone asking another person a question.
The second group consists of people who rarely ask questions, but simply launch into a topic of their own interest. For example, if they recently saw a movie or read a comic book that they liked (or disliked), they start talking about it. They ask few, if any, questions, and only about subtopics within the speaker's chosen topic, e.g., "Did you know that the actor in the movie I saw trained as a martial artist in Korea for five years?"
Eventually, another speaker takes a turn, with a monologue of his choice. Everyone seems happy. No one thinks anyone should have asked a question or that anyone monopolized the conversation.
I find myself very bored when I am speaking with the second type of conversationalist. My instinct is to just listen, occasionally asking a follow-up question, until they ask me something. It would feel very strange for me to suddenly launch into some topic of my own. It would feel like a non sequitur, and because I have just been bored by someone else's monologue, becoming the person who bores others does not appeal to me. I would rather be bored (temporarily) than be known as boring.
Is this a matter of personal preference, or does etiquette favor one type of conversation over the other?
GENTLE READER: These are not two types of conversation. Both you and your more tedious acquaintances seem to misunderstand the term. Conversation is an exchange involving two or more participants, after they have fished around for a topic of mutual interest.
Direct interrogation is not absolutely necessary, and some of the usual approaches -- "What do you do?" and "Where are you from originally?" -- are annoying to people who do not want to discuss their jobs or family backgrounds.
It is not wrong to start off with a statement such as you describe, provided there are pauses for others to reply, "Really? I heard it was terrible," or "Something like that happened to me once."
So your real question is how to get away from bores. No one has really solved that, but Miss Manners suggests: "I think I hear my mother calling me," if that is plausible, or "I'm going to get another drink. Can I get you anything?"