A false Christ isn't simply one who claims to be the one and only Saviour of the world, but can also be one who comes claiming for themself a special anointing from God and a corresponding authority to speak and act on God's behalf. Christ means "anointed one" and the visible church is full of people who boast in their unique anointing rather than boasting in Jesus alone.

Original video:
https://www.youtube.com/watch?v=-a_WGIdmyXU