I think a certain amount of extreme dominance is hereditary, and some may be learned. An extremely aggressive, dominate cow can pass on to her calves both her inbred attitude, but they also learn by watching mama cow push others around.
Have had some aggressive, dominate heifers around. Some were aggressive towards other cattle but fine with people, and some were not fine with people and you could never totally trust them when you were simply walking though the field, and had to keep half an eye on them.
Some cattle are "bluffers" will come stomping your way, but a wave of the arms and a bellow at them will send them scooting off, and you need to know which cattle are bluffers and which are serious.
Talking about pushy cattle, had a Semmental heifer put the run a full grown cow moose.
Saw the heifer flip her tail in the air and take off full charge at the cow moose who was about twice her size. The moose believed it and sailed over the barb wire fence catching the top wire in the process, could hear it sing an twang. She took off and never slowed down.
If you know anything about moose, sometimes they can be real aggressive and nasty especially in the winter when they are hungry and want that hay stack for their own, so I was very surprised to see that moose split for high country.
Had a different heifer, ( another Semmental) who was very aggressive and dominate, try to put the run on a very angry black bear who was beating the ground with his front feet and popping his jaws and foaming. She wanted to run at him even though he was on the other side of the fence! Not too smart. She was possibly saved by her greed, someone came out and shook a bucket of grain, and she forgot about chasing the bear.
I do believe that a certain amount of pushiness can be bred out by selecting for docility, and know of ranchers who have selected for years for calm cattle, and anything that "flicks an ear" gets shipped, and they do have calm cattle in general.
There will still be a pecking order and some pushing, but not the insane constant bashing that some cattle engage in.