You probably know that our brain processes quite a lot of information on a daily basis. Therefore our brain filters out a massive amount of impressions we are constantly exposed to, so we are not overwhelmed. Not only does our brain filter out many impressions, it also puts a spotlight on specific things and makes us sense those more than others. Example?
- you want to buy a new car and suddenly, you see this car way more often than usual
- you are thinking about getting a baby. Where are all the babies coming from out of the blue?
- you are a general pessimist. Guess why you don't see the good things in life.
You get the point.
This also applies for the behavior of other people (and therefore yourself). How people perceive you comes with a filter. I will insert the term cognitive dissonance here, assuming that most are familiar with it. It basically means that your brain rationalizes everything to fit into an existing box of what you are already thinking.
Example: For a person which you perceive as an arrogant person, you only see every action they take as a behavior of an arrogant human. Even if the person would do something nice, you will think that they might only have done it to use it as advantage in the future - but (s)he is still arrogant. You wouldn't consider that (s)he had the best intention in mind, because then you would need to readjust everything you ever thought about that person.
In case you have a bad habit or trait and want to change, it is a great first step to acknowledge your flaw(s). Even better when you are actually improving and changing. Considering that this was a flaw other people were aware of as well and not only you, it will serve you when you tell people that you are trying to change. Not only that you are trying to change something of you, but what specifically.
As soon as you promote this and advertise it, you help the other person to readjust their senses and perception of your behavior and put it into context why you react a specific way now. (Considering the other person actually cares about you, because you might have apologized about your previous behavior - that's another story...)
What makes them believe even more that you are serious about tackling your shortcomings, is when you ask them about ideas of how you could improve and show them that you really considered their thoughts. Additionally, telling and proving that you try hard will increase respect, understanding and empathy. And therefore success for getting people to see your change.