I can think of several reasons why spaces should be excluded; these reasons have nothing to do with security though but with usability:
If you transmit a password that have spaces in it, how does the recipient knows that it's a space or a tab? And is it one or two spaces? Assuming you have to hand-write it (it happens), how to show this information? Depending on the font of their email client, there's also a chance, they won't notice the blank space(s).
Again, when sending the password, if the spaces are at the beginning or end, it will be easily missed and will have to be enclosed in quotes. But even then it will look odd and I can easily imagine users not including this last space and being unable to login.
Blank characters (newlines, tabs, spaces) are often trimmed from the end and beginning of a field, to avoid people copying and pasting incorrect data. Obviously if the spaces were significant, that would cause a problem.
All in all, I think not having spaces avoid all kind of problems and saved support calls, so it is a good thing.
Edit:
To answer the comments about the bad practice of sharing passwords:
Let's say important business documents are locked on Bob's station, who is currently on vacation. What to do in this case? Wait for Bob to return two weeks later and lose potential business in the meantime? Or just ask him to send the password? It's Bad for sure but still better than the alternative.
As Linus Torvald put it (about something else, but I like the spirit): "you should deal with reality, not what you wish reality was".
