My macbook pro (OS 10.8.5) and iPad air 2 (set to "Airdrop:everyone") cannot connect with each other

See the System Requirements for AirDrop here: Mac Basics: AirDrop lets you send files from your Mac to nearby Macs and iOS devices - Apple Support

Your iPad Air 2's system requirements are fine (default iOS version out of the box) but your MacBook Pro needs to be a 2012 or later model as well as be running OS X Yosemite 10.10.

From the document I posted above see this:

System Requirements

To see if your Mac works with AirDrop, make sure you’re in the Finder by clicking the desktop (the background area of your screen), or by clicking the Finder icon in the Dock. Then, check to see if AirDrop is listed as an option in the Go menu. If you don't see AirDrop listed, your Mac doesn't support this feature.

In order to transfer files between a Mac and and an iPhone, iPad or iPod touch

• your iOS device needs to include a lightning connector
• your iOS device needs iOS 7 or later installed
• your Mac needs to be a 2012 or later model with OS X Yosemite installed
• Your Mac and iOS device both need bluetooth and Wi-Fi turned on. You do not have to be connected to a specific Wi-Fi network.

To transfer files between two Mac computers, you need the Mac models listed below with Wi-Fi turned on and OS X Lion or later installed.

• MacBook Pro (Late 2008 or newer)*
• MacBook Air (Late 2010 or newer)
• MacBook (Late 2008 or newer)*
• iMac (Early 2009 or newer)
• Mac Mini (Mid 2010 or newer)
• Mac Pro (Early 2009 with AirPort Extreme card, or Mid 2010)

*The MacBook Pro (17-Inch Late 2008) and the white MacBook (Late 2008) do not support AirDrop.

For help identifying your Mac, choose About This Mac from the Apple menu. You can refer to the Apple Support website to find out if your iPhone, iPad or iPod Touch includes a lightning connector.