Rebellion is when we trust in our own understanding, knowledge and experiences and not in God. It is when we do as we please and not according to what God has requested us to do.
Rebellion is as good as witchcraft in many ways. A witch or a magician believes he has the power to do the extraordinary or supernatural acts, to bring both happiness and misery in a persons life and many other things. Witchcraft is therefore all about a person believing he can do whatever he wants because he has the power to do so, just like Rebellion. When Saul rebelled against the Lord, by sparing Agag and the best of the livestock, he did so because he was in a position of power and thus could do what he wanted, even though a force greater than him had comanded him to do otherwise.
Arrogance is defined as an offensive display of superiority or self-importance. When Saul rebelled against the Lord's comand, he was indirectly being arrogant as he shows that he put himself (the fact that he is the king of Israel) above everything and everyone else.
I believe prayer and meditation on the word is the answer to all things. if we find rebellion in our hearts against God, we should do this at all times and find a way to listen to him when he speaks to us and to also do as he says and not what we want to do. If we do nothing we are going deeper in the life of sin that we already live in.