Why is Tony Stark so arrogant in the MCU?

Tony Stark is arrogant in every MCU movie; it's a key part of his character. In fact lots of male MCU protagonists are arrogant (i.e. Star Lord and Dr Strange as well as Stark).

Tony Stark is arrogant because he is, and has been for all of his life, incredibly, incredibly rich. That makes you believe that you can do anything (or at least, get anything done for you) because, usually, you can do anything with enough money.

Secondly, Stark is an exceptional inventor/mechanic. That's clear from the fact that he was able to make the first Iron Man suit almost solo (only had a little help from Yinsen), not to mention that he was trapped in a cave with only a bunch of scrap to work with [this happens during the first part of the Iron Man movie]. This would also bolster anyone's self-esteem: even without his money, Tony could still make a good livelihood and possibly start up a new company using his skill and a bit of innovation, should Stark Industries fail (which is extremely unlikely).

Stark's heroic successes as Iron Man also probably improved his opinion of his own awesomeness. (This may have been part of the reason for him revealing to the world his secret identity at the end of the first Iron Man film.)

It is worth mentioning, however, that Stark's big ego decreases somewhat as his story progresses in the Marvel Cinematic Universe and he realises that his selfishness causes serious problems for others. (This realisation can be seen throughout the Iron Man and Avengers films, to the point where, by Avengers: Infinity War, Stark's narcissism has almost disappeared - except when he comes into conflict with Strange, since they are both arrogant leaders who don't take kindly to being told what to do.)

The first flashback scene from Iron Man should tell you everything you need to know. He was a Wunderkind; he showed exceptional brilliance from a very early age, he grew up in privilege (which would make him a person to be envious of among his age group peers) and his parents were frequently away, so he was most likely a bit of a brat to his nannies or caregivers. Tony Stark was basically just that; a spoiled brat. He was a scientist/inventor with a professional athlete's attitude of "Yes, I'm better than you." And because he thinks he's better than everyone else, he believes he's the leader of The Avengers and so should and can make decisions without their input.

His father was brilliant but also an egomaniac and that was during the period of War so his genius was even stronger than Tony's & Tony's also an alcoholic which would give him mood swings and he does do the right thing like guiding the missile in the thing when in back into space when it benefits the whole group but it also, the Pepper Potts long story shows his shortcomings with other people and he tends to think of himself first and how his self-preservation would benefit all of the team and civilians but it's a step by step process beginning with himself. The missile he got it back into space Would have been self-sacrifice on his part but he is an arms dealer and weapons builder in the beginning of the MCU which if I sold weapons that would cause mass destruction I probably have an attitude to "the Jericho?

I believe I read that he is based on the aviator/inventor Howard Hughes who definitely in real life was sort of abrupt and, being very sure of himself, might seem arrogant to others. I suspect that many successful people in technology would indeed seem arrogant -- a more recent example is Steve Jobs.