I have no doubt that since time began we, as a species, have been rocking our little ones gently each and every night. Indeed it is arrogant of us, as 21st Century parents to assume it is us who have 'invented' the lullaby. Cast your mind back, what song did your parents or grandparents used to sing with you every night? My mum always sang 'Mockingbird' to me whilst my Dad favoured a more, shall we shall, broadminded approach, his favourite rugby song!
Hands up everyone who has ever been told to stop singing along by your child? Yep, it happens to each and everyone of us who have ever spontaneously dared to sing along with whatever your child is listening too. It might be a film, it might be their beloved Jellybeans Music Wriggly Giggly CD, it might an advert, it doesn't really matter to your child, you are interrupting them in a way they don't like and aren't happy about.
But, they are not channelling their inner Simon Cowell, they are not trying to hurt your feelings - they aren't really old enough to recognise that you will be upset or irritated, they are still primarily egocentric.