Here are my favorite things about Android.
Google services just plain work. I love the synchronicity of the Google Services. It creates a great user experience for me.
The flexibility of Android. The great thing about Android is you can make it your own experience. While some things require root, others don't (more on that). But basically, if you don't like the way something works or looks, you can find an app to change it. From launchers to icon packs, you can change just about everything with little to no effort.
The growth of Android. Android has become one of the fastest growing platforms, applications on the Play Store have passed over apps on iOS. It will only keep on growing as more Android devices are activated over any other platform worldwide.
The ecosystem. You've probably bought into the ecosystem with apps that you've purchased. If you switch devices or add a new device, all your apps are available if it's compatible with your device. On top of that, you are not tied soley on Google Play Store for apps, you can also install apps from Amazon App Market.
Rooting and Custom ROMS. There are a plethora of apps out there designed for rooted devices that will give you extended functionallity. Custom ROMS are a way to update your device without being tied to OEM/Carrier. A good custom ROM can increase the life of your device and give you a fresh look at it. Some have additonal goodies baked in.
You aren't tied to one device: There are hundreds of devices running Android ranging from affordable to spec monster beasts. Android Devices come in many sizes and shapes. If you want a larger screen size, you got the Note III at 5.68", want a smaller screen size DROID Mini is a great deal at 4.3". With proper research, you can find a device that will suit your needs and tastes.
Compitition: Compitition is a very good thing. You have the major players, Samsung, HTC, Motorola, LG, Sony... and smaller OEM's (or location specific OEM's) like Pantech, Asus, Oppo, GooPhone all competing for your dollar. Each one takes a different unique twist on Android. Samsung has TouchWiz, HTC has Sense, Motorola has been running phones near stock Android now. But because they all are saying, buy me! they all are trying to be better.
So the question is, why not stick with Android? My recommendation is, check out the HTC One.
Edit: Also can't forget other goodies such as NFC and Wireless Charging. NFC is a great way to transfer files and (if your carrier will allow it) use it for payments on Google Wallet. Wireless charging is awesome, I love being able to just set my phone down on a powerpad and have it charge. Android allows for rapid implemetation of new technology because of the sheer amount of new phones that can be released. Within the last 90 days the following were launched (this is not an extensive list); Sony Experia Z1, DROID by Motorola (Maxx, Mini, Ultra), Motorola Moto X, Samsung Galaxy Note III, HTC One on Verizon, Kyocera Hydro, etc... Because of all the OEM's releasing so many phones, they can test new technology.