[kevincox]

The benefit is that people often don't remember which email they used for a service. They check their "main" email inbox but don't remember that they used their student email address 8 years ago when they signed up. By providing a hint they know which inbox to check and don't get frustrated because the email isn't coming.

So it is a privacy tradeoff for better UX. If it is a good tradeoff will depend on how much you value each.

[Zambyte]

Why not just login to all of your email accounts in your email client?

[justcool393]

probably because fewer and fewer people are using a (non-web based) email client.