[Pheter]

iOS push notifications are created on a server and then sent to the users iPhone. This means that the server must know about the event in order to generate the push notification that you see on your phone.

When you send a message from WhatsApp to your friend, the message is not sent directly from your phone to his. What actually happens is your message is sent to WhatApp's server, which then generate a push notification and sends it to your friends iPhone. (Push notifications must originate from a server. Your friends iPhone cannot check for new messages, instead it is told when there is a new message).

In Sparrows situation, they have no control over Gmail's server, and so they do not know when a new email is received and therefore cannot send a push notification to the users iPhone. Sparrow could store everyone's Gmail credentials on their own server and regularly check Gmail's server for new messages for each of their users and, if there are new messages, send a notification to the relevant user. However, this would mean that Sparrow would have to store everyone's Gmail credentials in one place which has certain security implications and, understandably, they do not want to do this.