I don't think it is weird at all. I view gender as a facet of our spirit, an aspect of our soul.
When I was very young, I did not feel like a boy or a girl, even though I was told I was one. I recognized that humans are spirits that have living bodies, and those bodies are very different from one another. At that time, my feelings and sense of self would be called agender, but I didn't think about it, nor were there any terms to describe it.
As we grew up and hormones decided to play with our bodies, I became very alarmed that mine was not following the path that I expected it to. Others around me seemed unconcerned about theirs and even looked forward to a future of sex. I didn't know if they were okay with the changes they were experiencing, or if they were not in touch with their inner spirit, and did not know the difference.
It wasn't until I got into therapy that I had a chance to talk to someone who understands what gender identity is. It is not how we act, speak, look, or dress. Those are expressions of what we feel we are inside.
When society or circumstances force us to behave, speak, look, or dress in a way that is not in alignment with our inner spirit, disharmony results. Many people do not feel it or are not aware of it. For you, it is not the disharmony you feel, but the harmony you feel when you are doing something in alignment with your inner self. That is equally significant. It is an inner guide showing you the path.
It is not about male or female, masculine or feminine. Those are terms used to describe a concept for others to help them understand. But for those who do not experience the difference (dysphoria or euphoria), there is no frame of reference, so they don't understand. If you have never given birth, you cannot know what it is like to experience that. You can understand the words and concepts used to describe it, but that is not the same as experiencing it for yourself.
I think you are doing a good thing by exploring these feelings to understand where they come from and what they mean. Getting to know yourself is never a bad idea. Keep at it, and one day someone will say something that clicks for you. And all the puzzle pieces will fall right into place.