According to Calvinism, why does God give mercy to some and not to others?

Because of the sin committed by Adam and Eve, who represented all of humanity, we have all fallen short of the glory of God. We are all guilty of sin. We were conceived as sinners. And because God is holy, righteous and just, He will not let sin go unpunished. So, we are all going where we deserve to go, hell. The word state that God is not willing that any should perish. It is our enslavement to sin that is taking us to hell.

But God, being a merciful God, saves some from the punishment of sin so that He can glorify Himself through them. But He endures patiently with those who remain on the road to eternal destruction. Even through them, when one day He displays His wrath, He will receive glory through it. Every knee shall bow and confess that He is God. God endures with those who are prepared for destruction by their sins and Satan, and He will display the riches of His glory through those whom He graciously saved.

But He also warns us in Romans 9 that the Potter has the right to make from one lump of clay some vessels for honour and some for dishonour, and that the pots do not have the right to ask the Potter - why did You make me this? The only explanation we have from Scripture is that He did it according to the pleasure of His will. Other than that we cannot speculate why He did it. We do however see that the showing of grace towards some is directly connected to a love that He has toward those whose names were written in the book of life.

Dr. Leighton Flowers (a former 5-Point Calvinist) speaks about this often. Check out his writings and podcasts if you're interested in more information or to hear from former Calvinists. He and his guests often speak about pre/post views on Romans 9, Ephesians 1, and John 6.

I've included an example of his prior/post interpretations of Matthew 22:1-14. While a Calvinist he viewed these as one combined choice, now as three distinct choices the King makes:

1. Choice of His Servants from His own country, given a task of sending the invites.
2. Choice to send the invites first to His own country and then all others.
3. Choice to allow only those properly dressed.

1. Israel for which the Law, His word, and Servants would be sent (Rom 3:1-3, 9:4-5). Not because they did anything (Deut. 7:7, Rom 9:11)
2. Israel and Gentiles, all “bad as well as the good”
   The above are the “many are called” - this is not about individuals being chosen to salvation.
3. Those clothed in righteousness of Christ through faith. The choice is anything but unconditional.

“Few” and “chosen” are those who responded freely to the invitation through his unconditional chosen servants from his unconditional chosen nation.

Verses like John 15:16 or Paul’s encounter are linked with Choice #1, not with Choice #3.

Choice #2 shows that its sent to all, not ‘some individuals but not others’.

God is granting or enabling faith or repentance by sending out the invites to all.

Regarding Calvinism one should look at history:

John Calvin wrote, "Augustine is so wholly within me, that if I wished to write a confession of my faith, I could do so with all fullness and satisfaction to myself out of his writings."[1]

"This is why one finds that every four pages written in the Institutes of the Christian Religion John Calvin quoted Augustine. Calvin, for this reason, would deem himself not a Calvinist, but an Augustinian"[2]

Cary concurs, writing, "As a result, Calvinism in particular is sometimes referred to as Augustinianism."[3]

Augustine was a Manichaean for 9-10 years, prior to his conversion. Augustine "taught traditional Christian theology against determinism for twenty-six years prior to 412 CE. When Augustine started fighting the Pelagians he converted to the Gnostic and Manichaean view and taught that humankind has no free will to believe until God infuses grace, which in turn results in saving faith."[4]

Although earlier Christians taught original sin, the concept of total depravity (total inability to believe on Christ) was borrowed from Gnostic Manichaeanism. Manichaeanism taught unborn babies and unbaptized infants were damned to hell because of a physical body. Like the Gnostics, the Manichaean god had to resurrect the dead will by infusing faith and grace. Augustine changed the cause of total depravity to Adam's guilt but kept the Stoic, Manichaean, and Neoplatonic concepts of the human dead will requiring god's infused grace and faith to respond[5]

Manichaeanism:

In this pagan group, a non-relational God unilaterally chose the elect for salvation and the non-elect for damnation based upon his own desires. Early church fathers prior to Augustine refuted non-choice predeterminism as being pagan.[6][7]

Gnosticism:

These systems believed that the material world is created by an emanation or 'works' of a lower god (demiurge), trapping the divine spark within the human body. This divine spark could be liberated by gnosis, spiritual knowledge acquired through direct experience.[8]

Sources (additional contained within links):
[4][5][6]https://en.wikipedia.org/wiki/Augustinian_Calvinism
[7]https://en.wikipedia.org/wiki/Manichaeism
[8] https://en.wikipedia.org/wiki/Gnosticism
[1] Calvin, John. A Treatise on the Eternal Predestination of God. in Calvin, John (1987). Calvin's Calvinism. Translated by Henry Cole. Grandville, MI: Reformed Free Publishing Association. p. 38.
[2]McMahon, C. Matthew (2012). Augustine's Calvinism: The Doctrines of Grace in Augustine's Writings. Coconut Creek, FL: Puritan Publications. pp. 7–9.
[3] Cary, Phillip (2008). Inner Grace: Augustine in the Traditions of Plato and Paul. Oxford, UK: Oxford University Press. pp. 122–124.

In hardline Calvinist theology passages like Romans 9 and Ephesians 1 are extremely important and helpful in this discussion. In Romans 9:11 we see that these things are done simply so that,

"God's purpose of election might continue." (Romans 9:11 ESV)

This however doesn't seem to help, for we know not what that purpose is still. So then we can take a look at Eph. 1 and see that in v.5 that election takes place,

"...according to the purpose of His will." (Ephesians 1:5 ESV)

This still seems a little vague, but it is mostly through these two passages that Calvinist's conclude that it is simply God's work for the purpose of showing His sovereignty and to work out His perfect plan that He decreed from the foundations of the world. It is thus for the purpose of showing His mercy and love.

We could also take a look at the Conversion of Saul/Paul the Apostle in Acts 9 and see that God tells Ananias that these things must be done, for Paul was a chosen instrument that God wanted to use. So God chooses for the sake of their being an instrument in His plan, this however begs the question, why did God choose to use Saul and as an instrument? There were in fact much more likely candidates there.

Well, choosing a man like Saul certainly does show God's love and mercy and sovereignty, if nothing else. Ultimately, the question must go unanswered, for if this view of election and -- as the Calvinist's view it -- SOVEREIGNTY is correct, then it is simply because God chose for it to be this way and who are we that we should question the potter's plans for the clay.

In my humble, yet educated, opinion; this Calvinist view of election and interpretation of these passages (Romans 9:11 and Ephesians 1:5) are extremely misguided for they are not interpreted in light of Pauline Theology as a whole, nor in the light of the quoted OT passages.