Most email on the Internet is delivered all the way from the original sender to the end recipient in seconds. Many user experiences require this, such as password reset interactions or email address verification upon new account creation.
When email isn't nearly instantaneous, it's definitely upsetting to users and a violation of the norm. Email is only not instantaneous in well-managed systems when one of the parties is experiencing an operational problem of some kind.
There are exceptions to this, such as large scale marketing systems that deliberately send at a slow rate to avoid overwhelming recipients. Once deciding to actually send a message, though -- if not rate-limited by the receiver -- messages tend to arrive in the inbox in moments.
Email isn't that complicated of a protocol, when you get down to the mechanics of email delivery. Loading a web page is orders of magnitude more complicated than sending an email; there's no reason why sending an email would need to take longer.
their expectations are unreasonable. gmail, etc don't even manage that much of the time, let alone guarantee it.