Humor me. I’m dying to hear your explanation. Don’t worry. I’m pretty good at adopting a position just for the sake of argument. (And I’m pretty familiar with the mind frame of God’s wretched slaves.) Consider it a part of your mission's due diligence.
...oh well since you're dying to hear it I think I must. Nothing to do with getting it out of me.
In order to understand:
"And whomsoever Allah guides, he is the follower of the right way, and whomsoever He causes to err, you shall not find for him guardians besides Him; and We will gather them together on the day of resurrection on their faces, blind and dumb and deaf; their abode is hell; whenever it subsides We will add to their burning." 17:97
You need to understand the concept of the soul ie who YOU are. What you really are. A human is made up of two things. A soul and a physical body. The soul is real and is something that can talk to itself, reason with itself. Once created will exist forever. It has certain "properties". It cannot see or hear or touch or smell or work out calculations or create things. It experiences enjoyment, sadness, pain (not physical), compassion, humility, anger, peace, excitement, etc. Now to experience these things it needs a body. There is an interface/link between the body and the soul. In order to experience pain the body can be affected to cause pain. In order for the soul to feel happiness the body can affected to cause this. For example by showing it pretty visuals, sweet smells, soothing touches, etc. The soul can be given varying levels of intelligence where intelligence is measured by memory recall, ability to work out calculations, creativity, etc.
Now the soul also has desires such as wanting pleasures, feeling of importance, egotism, etc. the bad stuff. Some souls are always going to be like this. I don't know why but that's just how it is. Some souls will realise this and try to correct themselves. Some souls hate this and are really "good". When God says he will guide some and cause/leave others to err he is saying that he knows your soul and he knows whether it is worth saving from Hellfire. The souls that reach Hell will never correct themselves. They will say sorry but when you let them off/forgive them they will return to their bad ways. So even though the experience hellfire and are returned to earth they will go back to doing bad instead of making the effort to make themselves good. Why did God create a bad soul? I have no idea. That's just how it is.
The idea of a soul explains why most things in creation fear God. The earth, stars, mountains, animals, etc. all have a soul. There are verses in the Quran which mention talking ants and birds, rocks sinking due to the fear of God, mountains fearing God, sun/moon prostrating. It's bizarre and hard to believe, I know I've been there myself.
To kind of get an idea about the soul do this. Find a very quite place, close your eyes, and think. That's you the soul, the thing which is talking to itself. That voice in your head, your conscious.
Everything you have in the life of this world is temporary. The houses, cars, friends, kids, family, job, money, beauty, love, relationships, etc. For the vast majority of us everything in this life is to test your soul, to learn about God to learn who you really are.
So to summarise again the meaning of the verse only those souls which God deems worth saving will be saved. How can you save yourself? Be honest, kind, humble, caring, helping, gentle, fearing, patient. Don't mock, or be arrogant, selfish, greedy, materialistic. That way if as an atheist you are wrong you have a backup which may save you. At the end of the day you have nothing to lose and everything to gain.