Natasha thinks it's weird that Daniel looks ready to cry and thinks that new headphones could never replace her now broken ones. Samuel bought them for her not long after she moved to the US. He bought gifts for Natasha and Peter on layaway, even though he couldn't afford them. Natasha thinks she didn't care why he bought them; she just loved the headphones and worshipped her dad. She thinks her headphones are the only thing that know that she hates herself for no longer worshipping her dad.
The history of Natasha's headphones shows very clearly that even though she tries to hide it, she is an emotional person who at one point had a very deep connection with her dad. This makes it clear that her disdain for destiny and passion is a front and a way to protect her from feeling painful and unwanted emotions.