As a less contrived example then, consider "andix.hacker@foo.com" vs "andix..hacker@foo.com". Some email service providers canonicalize those to the same thing, and some don't.
Your service using emails for logins or adspam or whatever now faces a choice. You probably have to accept periods, and you probably don't want to try to hard-code all the different ways a period might be used legitimately as opposed to a typo, so you have to deal with that problem somehow. You can canonicalize (opening yourself up to hijacks, some unintentional as legitimate users just have emails that clash in your system), or not (potentially locking out some users).
Your service using emails for logins or adspam or whatever now faces a choice. You probably have to accept periods, and you probably don't want to try to hard-code all the different ways a period might be used legitimately as opposed to a typo, so you have to deal with that problem somehow. You can canonicalize (opening yourself up to hijacks, some unintentional as legitimate users just have emails that clash in your system), or not (potentially locking out some users).