I would think that "insensitive" meant that his other girlfriends thought he didn't care, or he was a total idiot or soemthing. Just something like that. I hope this helped a little bit love!
can you specify the play you're talking about
The Hate U Give is Angie Thomas's first novel about a teenage girl who grapples with racism, police brutality, and activism after witnessing her black friend murdered by the police. The book became an immediate young adult bestseller and was adapted into a movie shortly after its release.