Throughout the story of Egypt, we find that Paroh’s heart is hardened, after which he resisted overtures to release the Jews. How could Paroh have his free will compromised?
The question of Paroh’s free will is based on the presumption that Hashem hardened it – but this is not entirely accurate The Seforno explains that there are two verbs used in relation to Paroh – כבד, heaviness, and חזק, strength. Being described as חזק, strong, is not a bad thing by any stretch! A careful reading will show that – for the first seven plagues – all uses of כבד are in reference to Paroh acting in such a way. Where Hashem is acting directly, there is only חיזוק – Hashem gave him the strength to continue – but why
To understand what the story is truly about, ask yourself, what was the point of it all? To obliterate the Egyptians? Or to extract the Jews? Both events happened, but lots of other things happened too. Miracles are always as simple as possible, so why the extravagance of plagues that didn’t produce free Jews or defeated Egyptians? Why extend the Egyptian’s suffering
Hashem is very clear why, but it slips right under the radar. Hashem explicitly states the purpose of what is to come to Moshe, foreshadowing the first plague
וְיָדְעוּ מִצְרַיִם כִּי-אֲנִי ה, בִּנְטֹתִי אֶת-יָדִי עַל-מִצְרָיִם; וְהוֹצֵאתִי אֶת-בְּנֵי-יִשְׂרָאֵל, מִתּוֹכָם – Egypt will know that I am the Lord, when I stretch my my hand over Egypt, and extract the Jews from among them. (7:17)
Hashem announces that this is about making something known. Consider that Hashem’s power to this point was entirely unknown. What miracles had been performed that more than ten people saw? People knew about the God of their fathers, but there had never been “outstretched hand” type miracles in history – yet. Egypt – and the world – would know soon enough
This is why Paroh needed the חיזוק – he could not release the Jews because of the beating Egypt was taking; he could not give in for the wrong reasons. He needed חיזוק as he grew to understand the nature of what he was up against.
But after the 7th plague, the task is seemingly complete; Paroh concedes, completely:
יִּשְׁלַח פַּרְעֹה, וַיִּקְרָא לְמֹשֶׁה וּלְאַהֲרֹן, וַיֹּאמֶר אֲלֵהֶם, חָטָאתִי הַפָּעַם: ה, הַצַּדִּיק, וַאֲנִי וְעַמִּי, הָרְשָׁעִים. הַעְתִּירוּ, אֶל-ה, וְרַב, מִהְיֹת קֹלֹת אֱלֹהִים וּבָרָד; וַאֲשַׁלְּחָה אֶתְכֶם, וְלֹא תֹסִפוּן לַעֲמֹד – Paroh sent for Moshe and Ahron, and said to them, “Now I have sinned. Hashem is righteous; my people and I are guilty. Beseech Hashem, and bring an end to this fiery hail; I will release you, you will be here no more…” (9:27,28)
Egypt now knows, but the education is not complete. The subject changes subtly:
וּלְמַעַן תְּסַפֵּר בְּאָזְנֵי בִנְךָ וּבֶן-בִּנְךָ, אֵת אֲשֶׁר הִתְעַלַּלְתִּי בְּמִצְרַיִם, וְאֶת-אֹתֹתַי, אֲשֶׁר-שַׂמְתִּי בָם; וִידַעְתֶּם, כִּי-אֲנִי ה – So that you tell over to your sons and daughters, how I toyed with Egypt, with my wonders that I placed in them, and you will know that I am the Lord. (10:2
Now it is about the Jews. The Jews needed to understand what Hashem would do for them. A generation of slaves could scarcely fathom what was taking place – see the troubles they gave Moshe even after all this – Hashem wanted to show His care to the Jews.
This is where stubbornness comes in. Once Paroh had conceded and submitted to God, he needed stubbornness to resist anew. This had nothing to do with his free will – Egypt’s understanding is not referred to again.
This is וּלְמַעַן תְּסַפֵּר בְּאָזְנֵי בִנְךָ וּבֶן-בִּנְךָ – for us to internalize how incredible the events were, how much Hashem did and does for us.