The answer is trust. Only a full node guarantees that you’re actually interacting „with the blockchain“ and you communicate with the peers in the protocol of the actual network. The wallet balance is calculated from your local copy of the block chain (which must be constantly kept in sync to not fall behind the longest and valid version). For me it also helped to understand how blockchain technology and decentralisation actually works.

All other light wallets are just communicating over a proprietary application protocol with a regular server provided by some company. Your account balance is calculated there on the server and your submitted transactions go through „their“ hands. That is a risk.