Here is a "pure logic" reason why Jesus is God without quoting any scripture...
Things have to be done on the same level.
For example: if an American insulted the queen of England, then the president of America would be required to apologise to the queen on their behalf.
Basically, in order for Jesus' sacrifice to be sufficient for us to be forgiven for our sins against God, Jesus would have to be God, as there is none other on the same level as God.