Why did Jesus have the authority over people?

Answer 1

Jesus was (and still is) the Son of God, and as God in His own nature, He has authority over all creation, including every human being.

But Jesus never forced His authority on any human being, or has controlled humans to do His own will. On the contrary, Jesus was loving people, serving them and humbly suffering when they mocked Him, did not believe in Him and spoke against Him.
Even when they crucified Him, he did not say a word against them, just said: "Father, forgive them; for they know not what they do..."
Luke 23:34

Only over the demons or evil spirits, Jesus was exercising complete authority, because the demons are accursed for all eternity, and Jesus was using His power casting them out of the people, and in such way He started to proclaim the eternal judgment of all evil that God will do soon in fullness, when Jesus comes back on the earth.

Jesus respected the free will and the decisions of men. The same is today.
Jesus is God and King over all creation. But many do not believe in Him. Many mock and curse Him and live a life against Him.
And Jesus is still loving people, forgiving and patiently waiting for them to repent.
But when the end of this world comes, Jesus will use His authority in fullness and judge the whole world.

AnswerJesus had authority over the people because of his teachings to the people according to God's revelation of The Bible to him. His preachings were supported by miracles that he demonstrated by the will of God the Creator. He directed people to the right path of God, the one and only God. He called his followers to worship the One God, their Lord and his Lord. He warned his followers that who worships any other god than the God the creator he will be expelled from God's mercy and will dwell in Hell fire.

See the related question below for more information.