How is this related to webmail? That's just a choice regarding email clients. The matter of privacy and access are related to who has access to your email server.

"Webmail" generally implies that a large company owns and administers the server, and messages are stored on it indefinitely - in other words, completely out of your control and subject to the inherent corruption that centralization brings. Remember back in the day when you wouldn't take someone with a @hotmail or @yahoo address seriously? We shouldn't have stopped just because the domain changed to @gmail.