I second most of what Kohdy said.
I wouldn't consider myself a highly logical person at all, and I still felt this way as a kid. I couldn't wrap my head around the concept of my gender being different from my sex at all. I used to mistake mySELF for male all the time. For most of my childhood I had to correct myself in everything I did, 'no no girl's bathroom not boy's bathroom', 'no girl's line not boy's line', 'girl's team not boy's team' etc etc, because my whole life my instinctual understanding of myself has always felt MALE, and I naturally steered myself in that direction before I thought on it.
Even so I never thought anything 'odd' about this until recently. I had the same mentality, that I had girl parts so I was a girl. I was never happy with my body, and I was also ashamed when people pointed out my more masculine traits. I thought I was just unhappy because I was heavier than other girls, or not confident enough to wear girly clothes, or wasn't girly enough, or just naturally hairier etc.
It wasn't until college that I was really introduced to the idea of gender and sex being separate. Even then it's taken me years to internalize that and realize this was me, and all those things add up.
For a while I kept my embarrassed attitude about things people called me masculine for, but over time as my ideas about gender opened up, I slowly realized I was coming to LIKE those things, I started to feel GOOD when people said I had a manly attribute, and I felt this even before I knew it was because I was fitting my own natural idea of myself. I realized all those things I felt bad about were for the very same reasons you stated, because I was supposed to be female and I couldn't fit that category.
Everyone is different, and we all come to understandings in our own ways. For the longest time I thought because I had never been adamant and outspoken about this confusion as a child this made me NOT trans.
But only you can decide that. You're the only one who knows how you feel, you're the only one who can know if being male fits you right, it's up to you to come to your own conclusions. And try not to base it on 'standards' (including gender stereotypes) or other people's experiences, or even what other people think you are, because you're not them and only you know what fits you, and in my experience taking note of these things only hindered me.
It seems you're very aware of how your mind works, so that's a great start! It's not easy to open up your mind to things you weren't aware of before, and I can see it being especially difficult for someone with a more logical outlook.
So like Kohdy said, take a step back, and really look into yourself, independent of what others say and think of you, and take time to really think and feel it out.