Same way Castle got JEALOUS when Beckett was hanging with Damian his writer friend and now Beckett is definitely jealous over Sophia being his muse too!
she is supposedly not in love with him. So why is she so mad at him? Why is she so jealous like they are already a couple? I know I know... I am just going by her non-reaction to his love confession.
his love confession came at a time when she was getting shot and thought she was dying, hard to associate that moment with being a happy one. And at that point she did know she liked him but hadn't realized she was in love with him she was confused as she (and it's explained in the show ) is used to run away from relationships that might actually make her fall in love and be more than just liking someone (her walls). she only realized she loved him back when she did some soul searching after she got shot, and when she came back she decided to work on herself and improve herself (therapy and all) so she can get to a place where she could be ready to accept his love back and not ruin it by hiding away from him and shutting him down because she is afraid of opening up and being vulnerable. That's the plot of the fourth season actually. She didn't want to mess it up.