There are many points at which he gave that offence. It came up in different ways at different times. He commands even the unclean spirits, and they obey him. Equality with God was something he had to face during his temptations in the wilderness in the afterglow of his baptism and the affirmation from heaven that he was the Son of God. Concern to enjoy equality with anyone, let alone with God, is nearly always presented in a bad light in the New Testament.
Equality is represented as a concern with status, and something to let go, disregard or give up.
But there is one sense in which concern with equality was praised. The very point at which people resist ideas of equality in the one where it was specifically endorsed. Equality in possessions was mentioned by Paul as something good. It is in connection with the collection he made, from the many churches he had founded, for the poor among the faithful in Jerusalem. It was justified as a means of sharing things equally or make a fair balance.