You can't make someone listen to a full explanation.
In fact more often than not even if a person is silent they're not listening but rather (they're waiting for their turn) to talk.
If someone doesn't like what they're hearing they start formulating their own arguments as to why they are right and you are wrong.
Truth be told if someone asks you "Why?" more often than not it's a rhetorical question. They're not seeking an "understanding" of some kind. It's generally a "reflex question" to which they've already made up their mind that (there is no reason or excuse you could give them) that would "justify" your actions.
It becomes a dance exercise to make you sweat. Oftentimes you're better off to ask them why they are asking why? "Are you REALLY looking for clarification or seeking to understand?" or "Have you already made up your mind there is nothing I could say that would cause you to empathize with me or my decision?"
By asking (them) why they asked why can save you a lot of time and frustration.
If for example you cheated on me and in my mind cheating is a "deal breaker" then my asking you "why?" and your answer is not going to change my decision. Therefore my putting you through that dance serves nothing but to give me something to tell others your "excuse"
Writing is a long lost art but sometimes if a person gets an email or hand written letter without having a way to immediately contact the person they will take the time to read the whole thing. With time it may sink in causing empathy.
Nevertheless there are some caveats though.
A written letter/email cannot reflect the tone or inflection of a voice. People also have a habit of sometimes zeroing in on "sections" that upset them instead of balancing it within everything that was said.
Unfortunately it can easily be shared with people you may not have intended for it to be read by. This could cause one embarrassment.
Last but not least not everyone has the skill to write a letter or email that does not come off as defensive, angry, or blaming someone.
One has to know what their goal is. Are they looking to be heard or change someone's mind. You also have to show some empathy by stating you understand why they may feel a certain way about it (before) you offer your explanation.