Let me give you an answer to this that you can apply to every day life.
Say you steal $10,000 off of someone(I know you wouldn't but using this for an example). You squander it before they catch you. Someone comes in and repays that person the money(because you didn't have the money to repay it yourself) and the judge at court is witness of this. That person accepts the payment from that person and is satisfied with that. The judge then slams the gavel and sentences you to 15-20 years in prison. You would deem that judge cruel as that one person paid that $10,000 you owed back on your behalf. Yet, the judge refuses to accept that arrangement made between the three of you(you, the one you stole from, and the person who paid that which you owed).
This is why its utterly important to see how the atonement works. The atonement is an actual atonement, not a potential one. What I mean is that the Christ paid fully the debt His elect sheep owed. He paid it in full. If He paid for everyone w/o exception's sins, and then they are cast into the lake of fire, then God has done this even though the Christ paid their sin debt in full. He paid for them and then they, too, pay for them. That is double jeopardy.
So, if the Christ paid for someone's sins and God punishes them anyways, He would be no different than that judge in the above scenario.
I hope this helps you better understand our position on the atonement.