According to the "book" - take your pick which one - it is "god" who is depicted as doing the choosing. And the faithful appear to have various means of relating such "choice" with other words such as "God wills that all be saved." Other texts tell us "many are called but few are chosen", and others that "we were chosen before the foundation the world".
Which all creates the "mystery". If it is a matter of being chosen why doe snot a God of love choose all.
How does that create confusion. Yes God wills that all be saved. If He did not He would not have had His son arrange the preaching work now under way to save any who wish to accept it.
However He accepts that He is not going to get His way in all cases. After all, it is obvious, because if He always got His way this world would not be in the confused mess it currently is. However His original purpose will eventually be fulfilled.
He could, of course, force all to serve and be saved, but that would mean removing our free will, and He will never do that.
When Paul spoke of being chosen from the foundation of the earth, he meant as a group, not as individuals. The plan which is currently nearing completion was formed and announced in the Garden of Eden, though not in detail. However the very fact that Adam and Eve were able to fail Him proves that He does not predestine individuals. Again, to do so would be to remove free will, which He will never do.
Again that fits in with the overall picture, and God's personality.
Many will be called, because, as scripture tells us, and you mention God wants all to be saved. In fact many are being called at the moment, by people like me, who pass on God's word, His message, and the invitation to be amongst the survivors. However few will be chosen because few will choose to accept God's word and follow His son. they will be too intent on following the words of those who would mislead them, Apostate teachers.
In fact this is a perfect example of how you use the bible to interpret that bible. every scripture has to be understood in the light of every other relevant scripture, all has to fit the pattern of the whole, and even more importantly, all has to fit in with the personality of God especially His perfect balance of Love Justice Wisdom and Mercy.
That is who you come to understand the bible, and why it takes time and sturdy, as well as the help of Holy Spirit, to get there.