It’s like she had to completely unburden herself, separate Beckett from Kate, before she let herself break down. As if she couldn’t stand the idea that strong, invincible Detective Beckett could let herself feel that weak or vulnerable so she had to remove the things that made her Beckett (her signature leather jacket, gun, and badge) until it was just Kate in the hallway. Then, and only then, did she allow herself the moment to let the pain and fear take over.