Respect? It’s not a direct thing. It’s your reputation, and what happens when your reputation goes down. If you become known as someone who just plays with other people’s emotions, then that can have repercussions. People may not want to be your friend or get involved with you, or even trust you in the work place.
Breaking up by email just doesn’t seem serious. In a way, it’s stringing the person along. They wonder what the hell happened, and so they continue to try to bother you to get a satisfying answer to that question. If you break up in person, they can see how serious you are.
A lot of times, people have difficulty saying it straight. “We’re done.” “No, there will be no rekindling of the flame.” They try to let the person down gently (which is not a good idea since it doesn’t clearly say, “It’s over.”
Now I suppose that sending the “Dear John” email can allow you to say all that stuff without having to see the other person’s face, and thus make it easier to do. It’s like the way Pilots of Bombers feel. They let go of the bombs and they don’t have to see the carnage. It’s all clean. No fuss, no muss.
When you send a “Dear John” letter or an email, you’re doing what the bomber pilots do. You are taking the humanity out of it. “Dear John” letters were for women contacting men who were far away and were going to stay that way for a long time. There was no way to break up in person.
If you can talk to the person and you just send an email instead, well, people who find out will not think much of you. You will leave serious damage in your wake, and walk away without bothering to find out what happened. You’re just an aerial bomber. A person who doesn’t take relationships with the proper amount of empathy or sympathy. You become a person who is know as hard-ass and unreliable. And a coward.
If none of those things bother you, then you’ll use email. If you have some sympathy for the people you’ve been involved with, you’ll seriously consider doing it in person. It’s the honorable thing to do. Honor has to do with your reputation, as does respect. If you don’t find those kinds of arguments compelling, that would be a serious concern to me. I wouldn’t trust you as much. I’d think I’d made an error in judgment about your character.
That’s how serious it is. If there are a lot of people who think like me, you’ll find yourself marginalized or ostracized if you break up with someone that way. If you don’t care about your reputation, that won’t bother you. If it was me, I’d find that pretty compelling.