Why does my iPhone turn itself on after I place it in my charger and turn it off?

If the phone is powered off (as opposed to in standby), it will power on when connected to a charger. This is normal.

These are the reasons why your iPhone is turning on and off when charging.

1. Faulty charger and/or charger box.
2. Faulty battery. Go to a nearest Apple Store to replace your battery.
3. OS needs to be updated. Connect your iPhone to a Windows PC or Mac and install iTunes. For more information, go here -> Update software on iPhone, iPad, or iPod touch in iTunes on PC - Apple Support

If you want the phone to be off while your charging (though there's no technical reason to do that) is to plug the phone then turn it off.