Recently I have been observing the way people around me do things, and more and more I have noticed that my dad's shortcomings have become obvious, and now I realize why my mom is always prone to losing her temper, and it is largely due to my dad's stubborn personality that won't listen to advice.
Whether in his own home or when he goes to the elders' home, dad always loves to discuss the news with others, he can't see the housework in his eyes, and when he is asked to help, he responds slowly, so mom has to take on everything by herself, but dad still doesn't take it seriously.
Dad on the surface seems to be very good to talk to, but in fact, especially stubborn, they recognize the thing is a sinew, will not listen to mom or my advice, he also think it is we are too emotional, they are still happy to live their own lives.
For example, when he cooks, he has to eat heavy and puts in a lot of oil and salt, while my mom and I want to eat healthier, he thinks it's tasteless, and the next time it's his turn to cook, he'll double the oil and salt, as if he's trying to make up for it.
He goes shopping when he wants to, not caring what's left in the house, which often results in too many vegetables piling up, which go bad when they're not eaten.
He was particularly mesmerized by the TV, and he acted like he didn't hear me when I called out to him several times.
I suspect he's deliberately pretending to be busy to avoid chatting and getting down to business.

When I told my dad what was on my mind, he was always impatient and perfunctory or mocked me, and when I expressed my displeasure, he still thought he was right.
Sometimes he's so stubborn that when I say something to him in anger, he says, "You're always taking it personally, am I that bad? I didn't do anything bad."
I was so despondent at his indifference that I was often so angry that I couldn't eat.
As the old saying goes, whoever feels the pain has to change first.
It sounds like both you and mom are uncomfortable with some of dad's behavior, but dad doesn't see a problem with it himself, so it's you guys who need to adjust.
Sometimes it's the closeness that makes it easy to pick on each other, and I don't know if you're married or not, but if you are, that mentality might affect your married life as well.
You say Dad is stubborn, but have you thought about whether you yourself are stubborn to change him?
There are not two identical people in this world to begin with, and when someone tries to change us, even if we want to, it's easy to go against them because no one likes to feel controlled, especially adults. So, you are doomed to fail if you are bent on changing your dad.

A word of advice, at 27, try to be as independent as possible from your family of origin and start your own independent life, your parents couldn't have had a worse time, they have their way of getting along, don't get too involved. I feel like you're tied too tightly to your family of origin, is the relationship with your mom too symbiotic? I'm not sure, but only if you live on your own and step out of the box will you have a chance to see your parents for what they really are.
Mom's bad temper, on the surface, may seem to be related to Dad. We often think it's other people who make us unhappy, but it's really us who choose to be unhappy, run away or not face it. Of course, everyone grows up differently and behaves differently, and this is the part where parents need to grow up on their own. You can't grow up for them, but you can start by becoming independent and growing better yourself, and maybe influence them later, influence, not hard change.
Growth doesn't always come with age, and every discomfort is an opportunity to grow. Look outside the box and you'll see more clearly.