There are a number of reasons we would be prone to this.
You specify your father. You and your father get into heated discussions. So in this case, the elder, your father, is also prone to this. I doubt it is something he developed recently, so likely your entire life (like most of us, myself included) you witnessed that this is how family treat one another from the start. We have early impressions that stay with us, even before we can remember anything specific. This is called your implicit memory. This covers things like how you expect people to act, interact, how you expect people to treat you, etc. It forms from early infancy based on what you live day to day. It is what is said to be the reason that children that suffer abuse at very young ages suffer the consequences of that for life, even when they have been treated exceptionally as far back as they can recall. The chaos they experienced in early life will forever be part of their implicit memory.
Then you can go on to saying that all of this has likely, since your early childhood, been reinforced to you as appropriate behavior culturally. It is likely you have often seen similar things among all or nearly all the other families you know well. So then, this is reinforced as a very normal, expected way for family to behave.
Then there is human nature. It is very difficult to maintain being on one's best behavior at all times. As such, we are likely to allow our worst behavior to be done around and to those we are closest to for several reasons. One is that we have to function in society at a certain level to be able to live at all. You have to have income, you have to get assistance at times from others, even meaning through services you pay for (doctors, car repair, etc). If we were at our worst out in the world, we could effective alienate ourselves enough that no one wants to bother with is at all. So we cannot afford to do that. So we instead bottle up the junk and take it home with us usually. Then the other reason in part, I am sure, is that we have some level of expectation that the love and bond we share will grant us forgiveness for the bad behaviors. That is likely true for most of us.
You have to recall though, that treating one another well seems to be a relatively recent idea in family settings. In many places you are permitted to be violent to your own family with no recourse. Even where I am from (USA) it was permitted for men to beat wives and children for a very long time. It is only recently we have decided you have a right not to be hit at home. So we as humans have historically been capable of being pretty awful to those we "love" and seeing that even as normal and having it be an accepted practice within societies. There have been some cultures historically that were more like now, but many were not.
So I think there are likely a number of reasons we do it and the reasons we continue are most likely, like your saying, we accept that as normal. That said, I do not think we have to and have done my best to raise my family not to with relative success. My spouse and children are welcome to vent to me and each other and we do. We do try very hard to treat each other better than we treat anyone else. We have worked on things with communication and with boundaries and respect. I think our parenting approach helps us there, as we do not yell, we do spank, we do not take items from them, etc. We teach and mentor and lead instead, so we do not treat our kids like they owe us more respect than they are given nor that they are less than we are. I understand they need limits and guidance and they have been given those. They are not yet capable of making certain decisions and understanding the consequences of certain things. That is all covered. The difference is that I do use my position of authority to excuse me treating them ways that are less respectful than I would do with an adult. The reason I think this helps is it is far removed from how I was raised and it's work to not do the things that I was raised with. It is equally hard for my spouse. So when we are interacting as a family, we are used to already using thought, taking a step back, and being careful how we respond to a situation and once you are used to using this kind of thoughtful approach to your behavior, it is easier then to translate into all the ways you are interacting as a unit. My hope is that one day, when my kids are all grown (some are, some are young), that this will feel very natural to them to just do automatically, as it's been very hard for me and their dad to try to break that chain.
I do not want what I have said to make it sound like we are taught to treat one another badly. I think quite the opposite in fact. I think it comes rather naturally. I have had all my babies start to want to slap me when angry before they could walk. They didn't even have to be angry at me, but I was the one closest and there is an instinct for nearly all children to act out physically when upset (hitting, kicking, arching, etc). I would grab the hand, redirect, teach. I simply think we accept this part of our natural instincts versus trying to teach a gentler approach, they way we obviously would automatically start teaching our children not to hit us or one another. Instead, we have overall thought this is the way it is, so we haven't spent the effort it takes to help ourselves get past it.