You're making Jn 3:16 say way too much. God cannot possibly love each and every person in the world because numerous other scriptures say otherwise.
Furthermore, you don't understand predestination whatsoever. Predestination does NOT follow sinners' choice to follow Christ. You have that backwards, as well.
And you don't want to understand that your analogy is lame because it's unbiblical. For a biblical analogy, see my 4522.
When we came into this world none of us had any option to become anything but we inherited from Adam: a sinful nature, therefore a sinner! We came into this world
DEAD in our trespasses and sins (Eph 2:1, 5) AND in the uncircumcision of our hearts (Col 2:13). What part of
DEAD, don't you understand? Yet, you keep on portraying dead people as having the power of choice -- as though it's in their power to will themselves to life! This akin to saying that a barrel full of rotten apples has the inherent power to change themselves into good apples!

Yet, scripture teaches that we are
helpless,
powerless sinners (Mat 9:36; Rom 4:6). Scripture does not portray the human race as a small child who knows better -- is conscious and aware of better, but didn't do it. Dead people have no consciousness or awareness or power of ability.