Part of "showing a sincere interest in the other person" can be interrupting their monologue to ask them a specific question that redirects the conversation to

Part of "showing a sincere interest in the other person" can be interrupting their monologue to ask them a specific question that redirects the conversation to something of more mutual interest (or any interest.) You don't have to be a rug they wipe their feet on, you can stand up for yourself and what might be of interest to you, just keep it about them somehow. If they decide you're a horrible person 'cause they just wanna monologue about complaint X (not common, but it happens) or don't want any input from you of any kind including a question about them, it's time to move on. Most people just need a little bump to make them a better conversationalist. Most people do understand at some level that a conversation is a mutual agreement to discuss the matter at hand, and the agreement part is necessary.