Q: No Airdrop on iPad 2 w/ iOS 8.4

The iPad 2 (2nd generation) is not AirDrop compatible...you need an iPad 4th generation or later:

To share content with AirDrop, both people need one of these devices using iOS 7 or later, or a Mac with OS X Yosemite:

• iPhone 5 or later
• iPad (4th generation or later)
• iPad mini
• iPod touch (5th generation)

Source: Share content with AirDrop from your iPhone, iPad, or iPod touch - Apple Support

I fail to see why the iPad 2 is not compatible with AirDrop. It doesn't seem logical because all you need for AirDrop is WiFi or Bluetooth...

I believe it's the type of Bluetooth chipset and it's feature set. The older models are simply not equipped with the proper hardware as it likely didn't exist when the devices were sourced. Yes, the iPad mini is essentially a shrunken iPad 2 but it's newer than both the iPad 2 & the iPad 3 and was sourced much later.

Both the iPad 4 and the iPad mini were released in late 2012 and they are both AirDrop capable.