Note that though God said He would Harden Pharaoh's heart.. we see God doing this ONLY AFTER Pharaoh had already denied them leave. God fulfilled His word, but he had to in order that Pharaoh would not relent and He could show His power fully. However we KNOW God did not do this (hardening) prior because scripture tells us exactly when God hardened his heart, and is found after Pharaoh already denied them leave.
This goes to the same thing I state previously in 2 other threads.. God turning them over to their own desires. He hardens them AFTER they have chosen to deny him. We this summed up in 2 Thes 2:10-12 and many other places that speak to the same thing
I don't know why this is so mysterious to people, we experience this every day. The root of this problem is pride.
Some people are very humble and open-minded, while others are very arrogant and close-minded. If you debate with a humble person, they will at least consider your opinion. An arrogant person is very different, they will often become very obstinate and stubborn. I call it "putting up a wall". This is hardening. They are not going to give in no matter what.
With some folks, you learn it simply does not pay to engage in a debate. Their mind is made up, and they will not concede even the smallest point you might make. These persons often get very angry and abusive quickly.
The root of this is pride. And this was Pharaoh's problem. What was the very first thing Pharaoh said to Moses?
Exo 5:2 And Pharaoh said, Who is the LORD, that I should obey his voice to let Israel go? I know not the LORD, neither will I let Israel go.
The pharaohs believed themselves divine. It is not hard to imagine that Pharaoh believed himself a god. Therefore he was not going to submit to and obey anyone in heaven or earth.
We have all dealt with persons like this, and many times we ourselves act like this. We do not want to admit we might be wrong. We certainly do not like to believe ourselves inferior to others. Many times we react by becoming angry and obstinate. This is hardening. The more the other person pushes their point, the more angry and stubborn we become.
I mean, some folks get so angry they pull out a gun and shoot somebody. In my area we recently had a shooting in a sports bar where two guys were arguing about their favorite team.
This becoming obstinate is what is meant by hardening. You can imagine that every time God brought a plague on Egypt that Pharaoh was humiliated and embarrassed. He only gave in when he had no choice. If you notice in this account, it was always when God ceased a plague that it says Pharaoh's heart was hardened.
Exo 9:34 And when Pharaoh saw that the rain and the hail and the thunders were ceased, he sinned yet more, and hardened his heart, he and his servants.
Amazing, it was when God showed Pharaoh mercy and stopped a plague that Pharaoh became hardened. He was just an evil, arrogant person. It is very likely that one reason he went back on his word was simply revenge.
But we see this every day. We all know of someone you just cannot hold a discussion with because they will become angry and obstinate. If we wanted to harden them it is easy, just simply continue to engage with them. You can get some folks so angry they will try to harm you.
And this is all there was to it, God knew Pharaoh was very arrogant and full of pride. He knew how Pharaoh would react when confronted.
Exo 3:19 And I am sure that the king of Egypt will not let you go, no, not by a mighty hand.
God told Moses even before he went down to Egypt that he knew Pharaoh would not submit to him. And God knew Pharaoh would become more arrogant and obstinate when confronted. There is nothing mysterious or complicated about this story.