[Rey knows of two owners of this lightsaber. Only one is here, and he's long dead in her time. So she doesn't understand Obi-Wan's logic from that standpoint.

But the thing that really makes her temper flare is the blow to her pride. The lightsaber is one of the few things she can sense reliably in the Force right now, and she knows she has a connection to it. Obi-Wan's words almost feel like he's cheapening that, which hits her pride, and the ever-present scavenger in her rankles at the implication that it's not hers.]

It is mine! [She can't help raising her voice or the indignation in her tone.] It came to me. It called me! I feel this crystal as if it were a part of me! If that doesn't make it mine then what does??