Mail servers require a username and password authentication for outgoing mail (mail being sent from your computer to someone else) so the servers can maintain control over who is allowed to use the resource. The first, and probably most obvious, motivation is to control email spam. By requiring a username and password (which can be revoked), a company that operates a mail server can prevent spammers from sending massive amounts of email through its servers.
This provides legal protection for the company as well as a practical benefit: The mail server the company invested in, and intends to use, is not bogged down with spam email. We all know spammers don’t just send one or two emails — they send thousands.
In addition, since email accounts are typically provided as part of a larger bundle of services, such as website-hosting and Internet service, the companies want to make sure their customers have a secure mail server available. The average customer expects his/her incoming mail (email from someone else to the customer) to be safe, secure and accessible only with the correct username and password combination.
The company also has an expectation that only its customers will use its mail server. The most efficient way to ensure that is to require authentication for each mail transaction, whether it be incoming or outgoing email.