It's all about the intimacy
In order for Carmy and Sydney to happen, Carmy has to be okay with Intimacy and Sydney has to be okay with relying on Carmy in that way. I don't think Sydney has an issue with intimacy because we've been shown how she loves. how she cares. How she likes seeing people happy. She has shared intimate parts of herself with Carmy, marcus and i'm asuming Natalie. I think her issues may be in relying on another person if they can't show her she can rely on them.
Sydney and Carmy grew up differently.she knows love and care and afffection and unconditional love, and nurturance and protection. I think she is able to be intimate. I think she can be intimate with Carmen if he can give her the space to be. If he can show her she can trust him not with just being his partner, but in other aspects. (wink wink).
There have been pocokets of big time intimacy between these two, so the evidence is there they can both be this way with each other. For Carmy, he has to be okay with getting close. He' s just not. He can't be with the C person and whenever it seems he' s getting closer to Sydney, he sabotages in an unhealthy way. Because of the low-self esteem and the trauma, he can't see the benefits of intimacy. He also can't see how intimate he's been with Sydney.
You can see it in his eyes how close he wants to be. It's in his body with how calm he gets when he thinks of Sydney, but it continues to be out of his reach because he can't recognize what that feeling means. Carmy isn't completely lost though. i believe he has admitted to himself who he wants. What he wants, but the negative thoughts tells him it ain't gonna happen. You aren't worth that. etc. etc. etc. It sucks. But lets hope he'll find a path in season 4.