In Parshas Shemos, G-d's message to Pharaoh isn't so much, "Let my people go" as "Let my people go for three days".
While G-d's message to the Jews is that he will bring them to Israel, His message to Pharaoh is, "And now let us go, we pray thee, three days' journey into the wilderness, that we may sacrifice to the LORD our G-d."
Why does G-d tell Moshe to try and trick Pharaoh, a trick which doesn't work in any case? Since G-d already tells Moshe that Pharaoh will only let them go after a great deal of punishment has been meted out, why bother with the ruse?
To understand that, let's examine why Pharaoh didn't want to let the Jews go. Pharaoh's plan for enslavement begins with the fear that the Jews will escape Egypt. But why worry about the Jews leaving if they haven't even been enslaved yet?
And if Pharaoh wants to enslave the Jews, why does he then start trying to kill them?
If the goal is to rid Egypt of Jews because they are becoming numerous, letting them leave would have solved the problem. If the goal is to benefit from their slave labor, why kill them?
Pharaoh's behavior toward the Jews is contradictory. Moshe's three day proposal exposes that contradiction.
If Pharaoh is only interested in exploiting the Jews as slave labor, the three day proposal is no great loss. Especially compared to the economic losses of the actual plagues. When Pharaoh shows that he is willing to take great losses rather than let the Jews leave for a brief holiday, he is demonstrating that he is not motivated by economic considerations.
Pharaoh's response to Moshe begins with an extended rejection of G-d. He lashes out at the Jews as lazy for wanting to worship G-d.
The three-day proposal is not really intended for Pharaoh. It's a demonstration for the Jews, that Pharaoh is not just a greedy tyrant who wants slave labor, not does he just hate them as a purely xenophobic reaction. He would rather see Egypt destroyed than allow Jews to live by their faith.
What was the real purpose of slavery? Had Avraham committed a sin that his descendants were destined to descend to Egypt and be enslaved?
Egypt was a lesson. It was a lesson that the Jews had to live as a nation in their own land. Even the nicest exile would decay into hostility and hatred over Judaism. The Pharaohs might find Jews useful as financiers, officials and tradesmen, but no matter how they adapted, religion would always remain a source of friction.
The paradoxical hatred of the Pharaohs for the Jews embodied the contradictions of anti-Semitism. Pharaoh feared the Jews would leave, but wanted to destroy them. He worked them to death, but accused them of being lazy. He would rather see Egypt ruined than allow them to worship G-d.
When the Sages state that one who lives outside Eretz Yisrael, it is as if he has no G-d, it was recognizing the fact that Jews would not be able to fully worship G-d without their own nation.
Before Egypt, the children of Israel might have thought that they could go on as they were in a nomadic existence and still worship G-d, that they could have a religion and a people without a nation.
Pharaoh's refusal to even release them for three days at the cost of the destruction of Egypt showed them that the freedom to worship G-d is also dependent on physical freedom. To fully worship G-d, they also had to have the freedom to do by having their own nation.
G-d's three day offer to Pharaoh showed the Jews that Pharaoh did not just want slaves, but that his anti-Semitism was motivated by a hatred of their religion because of G-d. In later times, some Jews in the desert would complain that they had been forced to leave Egypt. The three day offer was a reminder why. If Pharaoh couldn't allow them to worship G-d for three days, then they could only truly live as Jews in an independent nation that would always leave them free to worship G-d.