Thank You, Cindy! This is very interesting yet slippery topic

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I hope my opinion wont insult anyone, but in case it does, then it is purely my views and only. I am a parent (father) of my lovely 4 y.o. and it entails all responsibilities which come with being a parent. Trying to emulate this into some sort of "mother-ish" feelings would borderline with serious mental issues (my view entirely), so I am not her mother and will never even try to occupy that position (I know that I potentially could but... she has one mother already and it is going to stay that way). I did not bear her and did not give her birth (when I was in teens, I often did wonder what it is like to be pregnant and pretended to be in a couple of cases... but when faced with reality I try to take pragmatic point of view - if something is not going to happen, deal with it, get over it and move along). So, I am her father, or as I prefer, parent, and I love her as much as I can, but I am not her mom (but I try to do my best in that regard, lol).
So, I try to give her the best and we have very open communication, but my biggest concerns are not about my triggers but about her safety. Because, when we are out in the public, people assume that I am her mother and treat me accordingly (I have even been congratulated on Mother's day, which I took but it did not feel deserved. Rather, it was another proof of passing). So, I dont want that later in her life she might be bullied or riduculed because her father is "that way" or for any other trans-related reason. I have given this a lot of thought and there are areas which are beyond my capability to control, but still, it is her safety and well-being which are of primary importance here, and if one day, for her own good, I would have to renounce my father status and become someone else (like, female relative who picks her up from the school), I will do that. That is the price which I am paying for my transition and that is the least that I could do.
On a completely side note, I sometimes think that becoming a father of lovely daughter was one of the last straws which took down deeply entrenched defenses against dysphoria - just realising that I will watch as she grows up and goes through her girl childhood, teens and adolescence, while I will watch it with deeply hidden jealously and envy, made me to re-think what was really happening all my life and why it never seemed to be real (like living in some guy's dream) and nothing was ever clicking together.
And sometimes I am thinking that having a daughter was the biggest blessing in my life, mostly, because she is the one who helps me to keep going. I only get to see her over weekends (or when I babysitting her during summer vacations when kindergartens are closed), but knowing that I will see her soon helps to survive those lonely and empty evenings and nights in between (but I have to admit that late Sunday evenings when the flat becomes silent and empty are the worst of that kind).