Twitter's reasoning is pretty dumb:

Imagine how nerve-racking – terrifying, even – tweeting would be if it was immutable and irrevocable? No one user is more deserving of that ability than another. Indeed, deleting a tweet is an expression of the user’s voice.

Imagine how nerve-racking - terrifying, even - giving a press conference would be if everything you said was immutable and irrevocable!?

Words that come out of your mouth can't be unsaid and words put up on the internet can't be undone, although people will certainly try. If you say something wrong, it's better to clarify, retract or apologize with an additional sentence, instead of pretending you never said anything at all.