Why would Jesus wait to reveal his Divinity until he was 30?

THE SHORT ANSWER: There was a plan. We don't necessarily understand the plan, but we recognize its presence in scripture. 

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Early in Jesus ministry, when he would cast a Demon out, they would tell the crowd who he was, It was almost as if they knew, Jesus was trying to keep his divine identity a secret, and they weren't playing along. Demons would say things like "I know who you are, The Holy One of God." So, it's like Jesus didn't want people to know. However, apparently the word got out in the spiritual realm about who Jesus was. 

For some reason, (we don't know exactly why) Jesus didn't want to people to know who he was at that point in his career. 

Around that same time, he healed some lepers. He specifically told them not to tell what he had done for them. The healed leper told everyone he came across. It says that after that point, Jesus couldn't enter towns, but had to stay out in lonely places. 

So yeah, I think Jesus knew he was divine, but it was part of the plan to wait until an appointed time. 

Think of when Jesus turned water into wine. It was his mother that goaded him into doing it. They were at a party that had run out of booze. Jesus' mother came to him and said, "they are out of wine." Jesus responded with, "Woman, it isn't my time." 

To me this means two things. His mother knew he had special abilities, even though this is the first miracle recorded. So his mother might have seen him do miracles before he went public. 

Second, notice that Jesus says "it isn't my time." so apparently, there was an appointed time that he would begin his ministry, and it hadn't come yet... even though his time hadn't come, he was still able to perform a miracle. 

To me it seems clear that he had the divine nature, but it was simple hidden until the appointed time. He was God undercover. 

John says in his Gospel, "He came to that which was his own, but his own didn't recognize him."