Exactly.
He fails to realize that he is arguing FOR love that precedes actions with his own illustrations.
Your point is the point.
Actions grow out of love. They are not love itself.
But Arminians are hamstrung by their propensity to conflate terms.
They think faith is the same thing as choice.
They think regeneration is the same thing as salvation.
They seem to lack the intellectual ability to allow each term to stand on its own.
Love is caring for someone. It is an emotion, but it is an emotion expressed through action. If you love someone, you treat them well, you do things to make that person happy, or things that will benefit that person.
If we see a parent who neglects their children, does not clothe or feed them, or does not discipline them when they do wrong, we suspect they do not have much love for their children, and rightfully so. You cannot see love except through action.
It is the same with faith. Paul said that whosoever calls upon the name of the Lord shall be saved. But then he asks, How shall they call on him in whom they have not believed?
Praying to Jesus to save you from your sins is not faith, it is evidence of the faith you already have. If you believe Jesus was simply a good man who lived and died 2000 years ago, you are not going to pray and call on him so save you. A dead man cannot help you.
But if you sincerely believe Jesus was the Son of God as he claimed to be, that he died on the cross for our sins and rose from the dead, and that he sits on the Father's right hand, then you will pray to him and call on him to save you. The prayer is evidence of your faith.
And doing good things to help others is evidence of love. It is a choice. Jesus did not have to allow himself to be taken in the garden, but if he did not allow himself to be taken and crucified we could not be saved. We would all die in our sins with no remedy. Jesus CHOSE to let the soldiers take him, he allowed himself to be crucified for our sins because he loved us. This choice was evidence of his love toward us.
If Jesus had chosen not to be taken and crucified, it would be evidence that he did not love us.