Wiktionary
vb. (context idiomatic English) Said of something that is heard but not attended to; (someone) failed to pay attention
Usage examples of "go in one ear and out the other".
Well, the people let all these announcements, decisions, and counterdecisions go in one ear and out the other, much like a preoccupied adult with the chattering of a child: well disposed at heart but unmoved.
Ham chimed in and explained to the manager that anything he said to Monk would go in one ear and out the other.
They were still looking back at her with respect (and a little fear), but most of what she had to say from this point on would go in one ear and out the other just the same.
I bet they listen when he talks, but they let it go in one ear and out the other.
But if you're anything like me, most of what I tell you is going to go in one ear and out the other.