If God only chastens those that he loves, and your doctrine says that he loves all mankind that inhabits the whole world, then why does he not chasten them? Your doctrinal theory does not harmonize with all of the scriptures.
You are right about God not chastening those that are not his; Psalms 71:5 says that the wicked are not divinely punished (plagued) like other men. That is because he loves his elect children, and does not love the wicked that are not his elect.
Isaiah 65:9, And I will bring forth a seed out of Jacob, and out of Judah an inheritor of my mountains, and mine elect shall inherit it, and my servants shall dwell there.
Rom 9:11, The purpose of God according to ELECTION might stand, not of works, but of him that calleth.