Update: Tried to do something sweet for my girlfriend and now we're fighting

Here is the Original post to catch up.

Thank you everyone for your comments. Took some to heart, others ಠ_ಠ, and some of us can relate to each other. I was totally in the wrong in not walking the dog and I dropped the ball. That was my fault...no excuse, I just didn't do it. After looking back, I over reacted but that does not dismiss my feelings or how she responded to them.

I went to her and apologize for overreacting and not walking the dog and she said her priority at that moment was to walk the dog (as some of you have said). She still doesn't feel like she did anything wrong. She is a logical type not a feely type of person and she said, "logically I didn't do anything wrong. I acknowledged what you did by saying thank you and it was sweet but the dog needed walking. The whole thing could have been avoided if you would've offered to come with me to walk the dog or say you'll wait for you to come back."

Yes I did overreact now that I look back on it. That is my problem that has been pointed out before by her. The apology turned into another fight about how she is tired of my overreacting and that she doesn't want to marry me if that's how I'm going to be. She said "I'm tired of worrying if I'm going to say something that's going to offend you because you're too sensitivities. Relationship is work but it's supposed to be fun work and this isn't fun. I'm about done here." She has used the if this keeps up I'm not going to marry you before. I've told her I don't like her bringing this up and I feel like she's dangling marrying me over my head. Her response to that is how will you know what I don't like if you I don't tell you. Cue fight #2, I said to her are you saying you want me gone because I'll be gone in 2 weeks if you want (let this be a lesson folks, not the right thing to say at all).

We both cooled down and talked. I apologized for saying what I did, which was a huge mess up on my part. It may have been too late. She said "I don't want a man who's going to run if I push him, I want a guy who's going to stick it out." Point blank, she's right. We ended it with us giving it another shot, but I really need to prove to her that I'm in this relationship.

Honestly I'm sick of our fighting style and we both act childish in how we fight. It seems i'm the common problem here though. I say that from thinking about other fights we've had. I know I overreact at times and I look at how I argue and it's similar in the way my dad argued. I need help changing that. Anyone else experience that or any suggestions folks?

tl;dr: Updated post and no sex for awhile.

edit: So from the comments I see, communication is bad between us, I need to dump her and move on, and we're not compatible. We are two different people, but does that mean we are automatically not compatible? I know communication on my part can be better and I need to work on it. When we're not fighting we are great together. Us being different I think sometimes complements each other, but our fighting is an issue. Perhaps it's a bad combination of her age and how I react.