The big difference between most people's relationship with their father and their mother (at least for us of a certain age) is that fathers historically were not involved in caring how their children felt. The traditional role of the father was to lay down the law of the house and to provide income. This comes all the way back from the initial formulation of the nuclear family, which was an imitation of the royal family where the king makes the rules and is responsible for the wealth of the land.

I provide that background only to point out that it is based on nothing other than folklore and fairy tales. It was a tradition that served its purpose but is not really necessary in modern times. You can be emotionally involved in your son's life. You can let him know how you are feeling, even if you are feeling weak or unsure. I can't say for sure, but I would investigate if you are more concerned about how your father feels about you as a person or if you are more concerned as to whether or not he thinks that you are a success. Is he the voice in your head that says "you can do it, I believe in you!" or "you better not mess up!"?

Part of this has to do with being emotionally competent yourself, which is something that you can work on.

I have a somewhat similar issue. He was never really present in my life (working too much etc.) and so we never connected. But he's also just a... somewhat unpleasant person to be around. If it's more than a few hours, it starts to get too much, so I rarely stay overnight in my home town. Recently (last Christmas) he's been making an effort to connect with me, but it's just so awkward and makes visits for me even more unpleasant. I just can't imagine ever connecting with him, no matter how hard he tries. (Doesn't help that he's recently started smoking again after like 15 years of being clean. I just don't understand it.)

It's most pronounced in my relationship with my father, but it's also my family in general. I feel a bit more connected to my mom and my grandparents, but I just can't say my family is very important to me, even if it sounds sad. My friends have always been my substitute family, in a way, even as a child, and it's even stronger now as a single adult. I probably spend more times with my friends from Norway (I live in Germany) in a single year than with my family in a decade.

Needless to say, this is also an unresolved issue for me. Not sure if it's possible to solve it other than accepting how it is.