I Am the Vine
On the surface, this may not seem as striking or outrageous a claim as "I am the bread of life," or "I am the resurrection."
Until we consider the immediate context, in which Jesus goes on to say "you are the branches," and anyone who – like a branch in a vine – abides in me will bear much fruit. But apart from me (because I am the vine) you can do nothing.
No other religious or political figure has ever claimed such a thing. To be the exclusive, all-sufficient source of fruitfulness. Jesus claims to be the only source of never-ending life the world will ever see.