The reason alot of them, a third [1/3] to be precise was that it was not a question of subordination but a question of soverignty, or the right to Rule.
Revelation 12:3& 4 tells us about the amount of angels that left God's side
3 And another sign was seen in heaven, and, look! a great fiery-colored dragon, with seven heads and ten horns and upon its heads seven diadems; 4 and its tail drags a third of the stars of heaven, and it hurled them down to the earth.
what was questioned in the Garden of Eden, was the Right to Rule;
Read the Following
Genesis 3:4-5 - "At this the serpent said to the woman: “YOU positively will not die. 5 For God knows that in the very day of YOUR eating from it YOUR eyes are bound to be opened and YOU are bound to be like God, KNOWING good and bad.”
Satan was Calling God a liar. He also stated that humans can be like God. Satanist now claim that they themselves are gods, which is exactly what the Bible said.
Anyways, you're asking about Whay Convinced them. Some were hesitant in the begining but some wanted to be worshiped like Satan. Its true that Satan Is called the Ruler of this world and he declare this himself when he Tempted Jesus
Matthew 4:8-10 - "Again the Devil took him along to an unusually high mountain, and showed him all the kingdoms of the world and their glory, 9 and he said to him: “All these things I will give you if you fall down and do an act of worship to me.” 10 Then Jesus said to him: “Go away, Satan!"
what about his Demons, his followers, will they get to rule with him, Satan? Yes as indicated by Daniel.
Daniel 10:2 - "2 In those days I myself, Daniel, happened to be mourning for three full weeks"
Daniel was sad and so God sent and Angel. in the following an angel is speaking to Daniel
Daniel 10:13 - "13 But the prince of the royal realm of Persia was standing in opposition to me for twenty-one days, and, look! Mi′cha‧el, one of the foremost princes, came to help me; and I, for my part, remained there beside the kings of Persia."
a human king cannot stop an angel and so this gives us an indication that it was a spirit creature, a Demon Prince of Persia. Co Ruler with Satan. They too had power to rule. Is there more? yes
Daniel 10:20 - "So he went on to say: “Do you really know why I have come to you? And now I shall go back to fight with the prince of Persia. When I am going forth, look! also the prince of Greece is coming."
Another Demon, but this time he is called the Prince of Greece. That is why Satan was able to tempt Jesus by offereing up what was his in the first place.
Trust me I've looked into this subject several times and when i was an Athiest i began reading books from diferent Religion and alot of them when compare are very similar Except the Biblical God, for they were the only MOnothiest (belief in one god) rather than polythiest (belief of Many Gods. ex: trinity)
What i came to understand is that it wasnt what convinced them but rather what they desired to have? God made Humans and Angels to Have free will, if not we would have been robots, but the ability to chose for ourselves. Satan was an Angel that had a very high standing before God but he chose to go up against God, and so must the other ones for they coveted being worshiped, praised, and some were just standing and watching all of this, doubt, envy and selfishness began to creep into thier hearts. They watched until they wanted it for themselves.