Every time I read
Merge branch 'origin/master' into master, or
Oops, forgot to commit changes, in a Git history, I die a little inside.
Of course I know why it is bad to clutter your history with these types of commits. Mainly because I have worked with both horrible and clean histories, and clean histories are simply better to work with.
But I'm also having trouble coming up with concise and convincing arguments why it is a good thing to maintain a clean and readable history, especially when arguing with inexperienced Git users.
So: why Is it important to maintain a clean history in general? Under which circumstances is it especially important?