A daddy by any other name

"Dad."
"Call me Daddy."
"Dad."
"Are you calling me Dad because last weekend Sam and Nathan called their Mummy and Daddy Mum and Dad?"
"Yes Dad."
"Right. Well in that case if you call me Dad I'll call you Nathan."
"OK Dad."
"OK Nathan."
"I'm Lily!"
"Hello Lily. I'm Daddy."
"Hi Dad."
"Hi Nathan."
"NO!"

I know that since, technically, I'm the grown up I should be the one to relent here, but I just can't. I really just can't.