Please help me to understand my father's rage

TW WARNING: Domestic violence

Growing up, my father has never been aggressive or hit my mother ever, but as he has grown older, he has become more sensitive to aggressive outbursts and occasional fits of violence. I 20f am at university now living in a different city from my family, and the last time my dad hit my mum (first time as well) was when I was 17, and they were arguing about me being rebellious and my father blamed it on my mother saying she was too soft on us and the reason why I was sneaking out was because she let me have my phone at night (the real reason was because I found out my father was cheating on my mother plus teen angst), and he ended up pulling her hair and shoving her and then the next day he apologised to her. Recently, today I got a text from my younger sister, who is 14, telling me our father tried to beat our mother up again, and this time the fight occurred because my father was berating my younger sister for taking her shoes off in front of extended family members while everyone else still had their shoes on (I know- very nitpicky and dramatic of him), my mother stepped in and defended my sister telling my father to calm down and that he is being dramatic and that not everything needs to be perfect. Then that is when he shoves her, and my mother says, "I will forgive you this one time, but don't you dare touch me again" which he responds,, I will do whatever I want", then proceeds to shove her into the ground and then into the wall and then he marches off and they haven't spoken all afternoon.

I have 2 other younger sisters as well who witnessed this, and as the parentified eldest child/daughter of my family, I feel a strong sense to protect them from any violence, and I am just really overwhelmed by all of this. I also have uni exams in 2 weeks, so this is adding a lot of stress. I am a very rational person and like to think about why or what caused this person to act the way they do. A lot of the time me my mother and I tend not to question or correct my father to try not to trigger an outburst, but I swear he goes around looking to pick fights or pick someone in the family apart. By the way, this doesn't usually happen, as my father is usually a bubbly, funny man, but when he gets angry, it's scary, and these violent fits of rage have only occurred twice in my whole life, but they are getting more frequent.

Please help me understand his behaviour. I am open to answering questions about my upbringing and his personality if it means someone can provide some sort of clarity with this.