Am I wrong for doing this?

I'll Set the story, basically my girlfriend started to become Cold with no affection towards me, she broke up with me 6 weeks ago, I've been tearing my hair out for absolutely ages trying to figure out but she would always say she just needed space, due to family issues I'm big on loyalty and not doing anything that could be disloyal, we were together for 3 years, OK to my main point, today while still trying to figure out why we broke up I decided to try guess her Fb password, I got it and saw she had been messaging and flirting with this guy a month before we broke up and even on my birthday she was messaging him all day and I knew it was flirting because it's exactly how she acted with me when I was flirting with her when we first got together. I confronted her about this because I'm big on loyalty and she erupted at me saying it was just banter, when she found out I had logged into her fb to find out she exploded saying it was a breach of her privacy (I completely agree) although it was good to find out why she probably broke up with me and it's all made sense and I wanted her to know what she did was wrong and hurt me, am I in the wrong? What would you guys and girls do in the same situation? I told her if it was me talking to a girl she would have rained hell down on me. Thanks guys.
Am I wrong for doing this?
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