There are very few professional businesses who contact customers and clients from a generic, free email address, and with good reason. The first impression a customer gets from a generic Hotmail or Gmail address is usually that a company is just starting up and hasn't focused on the public-facing aspects of their business, which can prevent a customer from really trusting the business they're about to work with. This is why professional emails are vital to any business who needs to contact clients or customers online.
Professional email accounts allow you to send and receive emails on an email address ending in your domain name (i.e. email@example.com) instead of the generic address (firstname.lastname@example.org) you might have otherwise. See the difference?