To her it's like losing an engagement ring. It's the sentimental value of the matching pair, it's one of the first things he gave her and is a symbol that they are a couple. Even when they argue all the time she still has that symbol to reassure herself they are a couple, that they can work things out. Or course, most engagement rings are expensive and meant to publicly declare and show off your a couple. But this was cheap but a intimate private symbol just between the too of them. In a way it's worth more than an engagement ring, emotionally.
I think he gets that on some level, but in the end what matters most is the two of them as people and all material possessions can be replaced. It's better if you home full of memories burn down as long as you family gets out safe, that's probably his logic.