How should guys handle arguments?

yannick
I've been in a relationship for a month and a half and last Tuesday, we had our first argument my girlfriend and I. The argument was settled quickly because she trusted me (the argument began on the topic of my ex-girlfriend) and she acknowledged afterwards that she had been mean to me when we were arguing, so for me, everything was going back to normal.

But since then, we've argued more often on minor topics and sometimes I am really not happy with the way she reacts and I don't know what I should do. We argued again on Friday morning on the way to a college trip so I told her that I was really sorry, that I understood her point and that it wasn't my intention to hurt her feelings and I asked what I could do to fix it. She got angry because she said that every time I did something wrong (it's funny to say that on the second argument), all I said was something like 'I'm sorry, what can I do to make things right?'. I was a little bit surprised because I didn't know there was a better way to handle an argument. If I did something wrong unintentionally, all I can do is apologize and try to do something to make it better. The subject of the argument being really minor, we just talked about it a little more and everything was okay again. Then at night, she got angry at me again. We were supposed to sleep in the same bed but at dinner, she introduced me to one of her friends and said that she would sleep in her bed that night. So later on in the evening I asked her if she would sleep with her or with me, because I was confused. She asked me 'Why are you always trying to argue with me?' and it really wasn't my intention to start an argument at all so I told her that I just wanted to know, nothing more. I left her alone for a while and later on I talked about it again, and she got angry again and said 'Can't I enjoy this moment?'. I was really caught off guard that she got angry at me so much in such a small period of time, I didn't know what to say and what I did wrong so I just figured that we would talk about it later or that she would apologize, but she never did. Before we went to bed, I just tried to ask her if she was angry at me and she said she was too tired to explain. The next day it was like nothing had happened, we were all over each other. Except that I stopped starting deep conversations with her, because now I'm afraid of her reaction. It feels like everything is going great if we're joking around, kissing, hugging or having sex, but I'm scared that if I talk seriously about my feelings or ask a serious question, I will say something wrong and she will get mad at me.

How should I have handled things? I really don't feel like I did something wrong, but I thought I needed someone looking at it from the outside to give me good advice.
Updates:
+1 y
I forgot something, she said 'Oh, so now I'm the one always making you confused. Can't I enjoy this moment?'.
How should guys handle arguments?
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