To what extent do we as humans have free will and to what extent has God predestined our lives?
I was raised as a Methodist so, I assume, I received lots of training in Arminianism. I don't think anyone ever used that term when I was growing up.
As a teen-ager I left the church. As I look back on it, I left because my church (meaning the church as it related to me) offered me nothing and did not speak to my needs. I considered myself an atheist at that point.
I attended a Presbyterian college so I definitely got lots of instruction on Calvinism. In the middle of my college years I returned to Christianity but not as a Calvinist; I joined a Lutheran church.
I can look back at my college years and recognize the importance of Calvinist teaching. I was studying science at the time and Calvin's theology was in total agreement with Newtonian determinism. The new scientific attempt to take down Christianity comes from a group of scientist that are Newtonian determinists. I was into science and I accepted Newtonian determinism. So I had lots of trouble with entropy and was in shock when I studied nuclear physics. But I did see in Calvin's teaching the agreement with Newton.
All that did not shake my new faith because it was based on resolving a contradiction. The koan would not have effected me had I not been raised as a Methodist and studied at a Presbyterian school.
Luther's answer to Calvin (and Arminius) is this:
If you are saved you were predestined to be saved - all glory to God.
If you are not saved it is your own fault - you cannot blame God.
That may not be "pure" Lutheranism but it is how the teaching was presented to me in a small Lutheran church in Illinois. I now realize that that was a koan. A koan, as I use the word, is a statement that has truth but is illogical. Such statements are meant to be meditated on. The meditation leads to deeper understanding, and, hopefully, enlightenment.
That koan brought me back to Christianity. Taking that path back means my faith is not based on some theological understanding. My faith is based on a truth that cannot be understood. The power of enlightenment.
Am I Calvinist? Am I Arminian? Am I Lutheran? God knows.