I'll skip the IOC flimsy explanation about how they determined which sport to remove based on TV ratings, international involvement, and ticket sales. I understand that on all three evaluation criteria wrestling beat modern pentathlon and still got removed. So that evaluation is a crock.
As I see it, the real reason the IOC dropped wrestling is that it doesn't fit in with the way the IOC likes to view sports. All the IOC members are fabulously wealthy. Their contact in sports is greatly influenced by their country clubs and grandchildren in prep schools. They don't gather at nearby parks for pickup games. That explains their recent decisions with which sports to add and remove from the Olympics. They've added tennis, golf, and rugby. They've removed baseball, softball, and now wrestling. They've added country club & prep school sports and removed those that are not. The IOC will add a sport for the 2020 Olympics, the first without wrestling. The new sport will be one of the following: karate, wushu, roller sports, speed climbing, wakeboarding, wrestling (fat chance!), and squash. Hmm. Squash is the only country club sport being considered. I wonder which one will get added...
You have probably detected my disgust with the IOC on this matter. The notion that one sport had to be removed was wrong, and that the one sport should be wrestling was even more wrong. I still cringe when the Olympics award medals for rhythmic gymnastics, synchronized swimming, dressage, and curling. Don't get me wrong, to some extent, I enjoy watching those sports. But that doesn't mean they deserve equality with track & field, swimming, or wrestling.
I'm an Olympics junkie.