Apple and Google have always butted heads because they're competing companies. Google has ownership stake in the Android platform, Apple has ownership of the iOS platform. They both want to have the most market share that they can possibly have, and if Apple allows Google Wallet, then it makes it easier for users to switch over later to an Android device.
It's all about stifling competition and not really about making the best product for the consumer. Profits, profits, profits, and always, profits.