American society so often frames emotion and logic as opposites battling for dominance. One of my favorite webcomics once framed logic as a leprachaun trying in vain to tame and ride the grizzly bear of emotion (please treat yourself to the adventures of Dr. McNinja). It is a fun image, and we do often feel like we have to choose between what we want and what we think is logically good for us. However, I don't think this is an acurate understanding of ourselves, and it can lead to some really unhealthy veiws.
Logic is great! It's a way to figure out almost any puzzle or question. It allows us to figure out how to reach our goals, and what those goals should be based on what we value. That last bit is super important! We need some system of value in order to make logic work. Emotion makes up either all or the vast majority of our value assigning system.
The first time I dissociated, it was hardcore. I felt absolutly no emotion. I had no opinions on anything, and nothing felt real or at all meaningful. However, I could do math and school work just fine. All of my senses were working properly. My only cognitive problem was that I had no motivation to do anything. Even when I felt pain, the only thing pushing me to do something was the idea that I'd care later on. I mostly just laid down on the floor and stared ahead motionless. The idea that an emotionless human being would be some super competant murderous monster seems frankly rediculous to me. Without emotion there isn't any reason to do anything, and murder requires a lot of motive, especially if it's premeditated.