-다느니 means "saying that..." or "with the remark that...", typically enumerating multiple remarks with a sense of "and so on" as when someone says different things in a disorganized way. It is kind of like like "... and ... and what not [and so on / and all that]". "서로 경우 맞게 말을 잘 해야 한다느니 그렇게 말해서는 안 된다느니 하는 .." => "서로 경우에 맞게 말을 잘 해야 한다느니 그렇게 말해서는 안 된다느니 하는 .." ("경우에 맞게": being fair for the circumstance and to all parties involved) "Saying one must make a persuasive yet considerate contention in one breath, then arguing one can't do that in the next...". "Remarking one must make a persuasive yet understandable appeal and then saying one can't do that and what not ...".

like such as, or That's what it means^^