THIS IS A VERY POWERFUL STATEMENT: Jesus is claiming that He was sent by God. This is language describing a prophet or other person authorized by God. His authority comes from God. He is claiming to be God's representative, with all the authority and power of God to accomplish the task for which God sent Him.
Imagine a person sent by a powerful King. If you insult or harm the king's representative, is it the same as insulting or harming the king. Having been sent by the king, his representative, his ambassador, has all the power and authority of the king.
They claimed God as their father. But their hatred and blood-lust prove that they are not from God. If they were from God, they would do His will. Their desire to murder a person whom they could not convict of a sin deserving of death, demonstrates that they were not from God. Jesus exposes them: "If God were your father, you would love Me". If they were from God, they would love Him because He came from God. In a manner of speaking, they would be brothers.