Why does he give us free will? So that we can choose to love him, because he loves us.

Yeah no. In Islam God gives us free will because we chose to have it. He offered it to his other creatures but they all refused fearing the consequences except man. God even criticises is for this choice. Here's the relevant verse from the Quran

Indeed, we offered the Trust to the heavens and the earth and the mountains, and they declined to bear it and feared it; but man [undertook to] bear it. Indeed, he was unjust and ignorant.

Quran 33 verse 72.

So why did we humans accept the trust? Because we wanted to be better than all the other creations of God. The angels and animals all don't have free will. They have to worship God whether they like it or not. They have no choice. However since man perfectly has the to disobey and rebel against and still chose not to do that but to obey him and follow his will then he's better than the angels.

This is why the consequences for disbelief are severe for humans and the pleasure and rewards they will get in the afterlife if they obey God and their own nature are superior and unlimited.