-냐며 reports the question somebody threw out, usually as the reason they acted: 오늘 왜 자기를 안 불렀냐며 'demanding to know why we didn't call him today.' It also carries complaints — 왜 따뜻한 우유를 달라고 했는데 찬 우유를 주냐며 'asking why they were given cold milk when they asked for warm.' The person's words are being relayed, not the speaker's own question.