For this Post, I want both sides of this debate to be open minded to the fact that men are prone to error, even good men led by God. I will keep this brief and elaborate more if need be.
A Brief History of the Problem:
With the reformation a number of doctrines of the Catholic church were re-evaluated and reformed based on the principles of Sola Scriptura. One of these was the prayers and veneration of the saints, a concept which no true saint wants in their life nor in their death but instead would rather all Glory Go to the Lamb that was slain and His blood that transforms and cleanses us. For example, scripture tells us to pray FOR the saints, not pray TO the saints. This reformation was fully justified yet in the process they threw the Baby out with the bathwater.... which is the distinction between the faithful and the saints (Ephesians 1:1). In so doing Protestantism deemed all believers as saints and from this doctrine alone comes the division of Calvinism and Arminianism.
What is the difference between the faithful and the saints?
The one big difference between the faithful and the saints is the fact that a saint does not choose to be a saint but is chosen by God to be a saint (2 Peter 1:1), whereas the faithful choose to be faithful of their own free will based on hearing and the word of God (Romans 10:17). Without this distinction, you will end up with two groups of believers, that believe that salvation is either by predestination or free will ("Whosoever believeth" John 3:16) and this is what we saw transpire once this error took root in Protestantism.
Why this solves the Problem:
If salvation is by freewill to whosoever believeth, then the Arminian is correct, but if those believers being chosen by God to be saints is correct then the Calvinist is also right, but each is wrong in applying their view on the other group, saying salvation is by predestination as the Calvinist do, or that becoming a saint is by free will as the Armenians do. Thus, the problem is failing to distinguish between the faithful and the saints in these churches.