“At midnight the Lord struck down all the firstborn in the land of Egypt, from the firstborn of Pharaoh who sat on his throne to the firstborn of the captive who was in the dungeon...” – Exodus 12:29
In one plague after another God devastated Egyptian homes, crops, livestock, and water supply... even a pandemic of physical disease spread across the land by the finger of God. But regardless of the devastation none of them were compelling enough for Pharaoh to truly change his mind. That is, until plague number ten arrived.
But why did this turn out to be the deal-breaker for Pharaoh? The general interpretation, which includes the numerous films made of the exodus, seem to have an implicit understanding along the lines that this was the one plague that actually ‘hit home,’ so to speak. The tragic death of Pharaoh's very own son. Some of the films in particular attempt to show a deep love for his child, and a supposed emotional brokenness over this situation. And in this emotional brokenness everything has shifted his mind to now release the people of Israel. Pharaoh is strangely even presented as somewhat of a victim of this family tragedy and presented in a markedly sympathetic light...This unfortunately seems to be a common but unlikely interpretation that doesn't follow well the historical or biblical picture. Historically, unlike our modern age with modern medicine, the death of a child in the ancient world was quite pervasive and regular. In ancient Rome for example the child mortality rate was around 50% who would not make it to ten years old. Of course this is not to say that Pharaoh would not have had an emotional reaction to his death, but looking closer there is more going on than just the loss of a son. Notice first, it is the death of his firstborn son. This son was of course the heir to the throne. And thus God was effectively cutting off Pharoah's ruling dynasty and the designated line of succession in one night. This is implicit not only in the fact of the son being his firstborn, but the text mentions this reality explicitly: “the firstborn of Pharaoh who sat on his throne.” The fact that his son was “on the throne” in some sense, might also imply that he was already an adult who had some measure of rulership already. Regardless, at the very least it means that this final plague would have been primarily a statement to Pharaoh about the impotence of his supremacy and his rulership, not primarily about family tragedy.
So what motivated Pharaoh to finally release Israel? I agree that it was something that ‘hit home.’ But it is less about Pharaoh being a heart-broken father with a deep love for his son, and more about Pharaoh's rulership being dramatically subdued in a most humiliating way. He is no god, his successor is struck down, and now he finds himself coming before the God of slaves to ask for a blessing (Exodus 12:32). There is a bit more to that one night that finally changed Pharaoh's mind.
ˡ There is a brief summary of this idea in Kenneth Laing Harris, ESV Bible Commentary, 156.