Topic: How do I be more

I've been in a relationship with my girlfriend for nearly four years. We're generally happy and in love. But at times when she's upset or sad or whatever and comes to me for comfort, I can't seem to help her feel better. There's two reasons why I think I don't help:
1) Because my idea of feeling better is more factual. Like I make myself "feel better"--although I'm usually never down anyway--by looking at the facts, realizing that it's pointless and that there's no basis to be upset. So I tend to present her with facts, and (in her words) "tell her how to feel" by saying stuff like "there's nothing to worry about" or "no reason to think that".
2) I think she can just feel it and hear it in my voice that I don't understand what she's feeling. She's told me before that other people make her feel better by just talking to her about anything, but I don't do that for her. That it's nothing I do or don't do, It's just me.

I've always known there was something wrong with me, but only recently found out that it's probably Alexithymia. I feel so bad because I love her and I want to be able to make her feel better and be a shoulder to cry on. But my only means of doing that are hugs, kisses and gestures. But if we're on the phone and she wants to talk I have nothing to say. The annoying thing about it is that when she tells me that I'm not helping her, I just get into bouts of rage, but not towards her. Usually I'll wait till we stop talking, put down the phone and break things, punch walls and If i'm alone or in my car, scream. I don't know why I get mad, and I'm not mad at her, I just get this feeling of desire to be destructive. She would also tell me that I either lecture her (what i said above), repeatedly say "yeah","I'm sorry", or "oh", or she says that I just make the conversation about me. I don't understand what that means.

I love her so much, (that i know for sure) but I can't just let our relationship be like this; where she can't come to me for comfort. I wanna be better for her, for Christ's sake we're already talking about getting married. If anyone could help me understand how to deal with comforting her, that would be the greatest thing ever.