The first reason is the price. The most important reason to choose Android. When Android tablets first launched they had a huge problem: they were not as good as iPads, and the good ones cost as much if not more. Cheap Android tablets used to be a synonym for 'terrible heap of junk'. But over the past couple of years that has changed significantly.
You can also find variety, and escape from the 10in slate design so popularised by Apple. From 6in phablets, through children's tablets, up to hybrid devices such as Asus' Padfone: there is more variety in the Android world than there is Apple's iOS platform. Even more than in the Windows world.
The Kindle Fire HD is a very different device from the LeapFrog LeapPad and the Nexus 10: but they are all based on Google's Android platform. And remember that Apple was once opposed to the 7in size of tablet popularised by Google- and Asus' Nexus 7 device. You could argue that the iPad mini was inspired by Android. That couldn't possibly be true, could it?
There are some other features available to Android tablets that you won't find on other platforms. These aren't available on all Android tabs, of course, but if you want wireless charging, or NFC, you need to look at Google's platform. If you want a kick stand such as that offered by the Lenovo Yoga tablets, Android is your only option (Ok, along with the Microsoft Surfaces). Or, being banal, how about the Tesco Hudl's integration with your shopping basket? These speaks back to point 2 above, but if you want something different, the Android world is where to look.
The Last Reasion is iPads are so 2011.