This is how it's suppose to be with a Gmail account.
When you add a Gmail account its settings are automatically different from the other accounts. Why? I have no idea, this is how you change some of its settings tho. (tho its not what you want

)
Settings> Mail, Contacts, Calendars> Fetch New Data> Advanced>
Now that does not show you how to fix your problem, it only shows that unlike the other accounts, where you can select "Push", you only have the choice of "Manual" and "Fetch". Make sure "Fetch" is checked, if that is truly what you desire.
Now go back to where you see the "Push" toggle.
Now you can choose between 4 options for your Gmail account.
1)Every 15 Minutes
2)Every 30 Minutes
3)Hourly
4)Manually.
Now since all your other accounts are most likely setup to Push in "Advanced" settings, these 4 options only apply to your Gmail account.
Since you want to be notified as soon as you get an email (which you cannot do
With a Gmail account) you have no choice then to check the "Every 15 Minutes" tab.
This will not notify you as soon as you get an email, but instead will check the account very 15 minutes.
Despite what you may here, the "Fetch" option drains slightly more battery than "Push". But since you cannot choose Push for a Gmail account, you have to either choose when you want your phone to "Fetch" the potential incoming emails, or simply keep "Manually" checked and just open the Mail app when you want to check your Gmail account.
It is recommend that you choose to manually check this as it saves more battery than Fetching.
But to really answer your question.....Apple (for whatever reason) decided that they would not give Gmail the option to have emails "Pushed" to the device, no matter what the settings.
I just keep my Gmail account on manually. Saves more battery.