Most web services want to be able to contact users, and use email for that. In particular, the user forgets their password, the fact that they can read an email at the address the service has on file authenticates them as the legitimate user, who is allowed to reset the password. Email can also be a way to inform you of important updates (a.k.a. spam you).
In order for the service to validate the email, it must ensure that the user who is creating the account does have access to that email. This is both to protect the user against a typo in the email address, and to protect the site's ability to spam.
You don't have to require an email to subscribe to your service. However, when users forget their credentials, they'll be unhappy. Email password resets are the norm.
If the user chooses a disposable email address, it's a deliberate choice from them not to have exclusive control over the account. Some sites that want to spam try to reject such addresses, although it is of course futile (big sites like Gmail also let you create disposable addresses, after all).