1 John 2:1 "My little children, I am writing these things to you that you may not sin. And if anyone sins, we have an Advocate with the Father, Jesus Christ the righteous; 2 and He Himself is the propitiation for our sins; and not for ours only, but also for those of the whole world."
Limited Atonement is a false doctrine, Christ did not just die for some, He died for all.
Pointing at the fact that many will not be saved has nothing to do with whether Jesus died for all.
According to Calvinism Christ only died for the ones that God chose to be merciful to. The rest He decided not to be merciful.
Does God desire all men to be saved? If so then why are not all men saved?
I can turn the question right around to you as an arminian:
If Christ died for all, why are all not saved? His sacrifice is either applied to all so all are saved or it is applied to some so only some are saved. Which is it? Both Calvinist and Arminians believe the same thing - that the atonement is applied only to some and not to all or else all will be saved and we know that's not the case.
God desires all men to be saved. That's His revealed will. But there is more to it because not everyone is saved. There is His secret will - that has something greater of importance than all might be saved. Romans 9 tells us that it's because of God's glory that some are saved and not all.