Why do Calvinists believe that God’s saving grace is irresistible? Simply, if God’s saving grace was not irresistible, no one would be saved. The Calvinist or Reformed Christian believes that Scripture teaches that the natural fallen man is dead in his sins. The natural man is without the ability to discern spiritual things, let alone choose to believe and trust in the Lord Jesus, to believe that He died for our sins, was raised from the grave on the third day, and is alive today preparing a place for us in the heavenly realms. Even godly sorrow, necessary for true repentance, is not natural and requires the grace of God.
Thus, Calvinists believe that salvation is entirely a sovereign work of God. Hence God’s sovereign election of those sinners to whom he shows His mercy and extends His grace is necessary that anyone be saved. Salvation is solely a work of the Holy Spirit in the hearts and minds of men and women whose minds have been blinded to the truth:
The god of this age has blinded the minds of unbelievers, so that they cannot see the light of the gospel of the glory of Christ, who is the image of God.
But without reading what John Calvin wrote, from the way Calvin is referred to in the history books, and commonly referred to in the public sphere, one could conclude that Calvinism is uniquely Calvin’s own doctrine of grace, somehow different from what the Bible teaches.
Hardly. Calvin relies on Holy Scripture, Paul primarily, and Augustine’s anti-Pelagian writings (in which Augustine also relies on Paul), when he develops his argument for sovereign election of the saints, God’s chosen elect. In this selection from Calvin’s Institutes of the Christian Religion (trans. Henry Beveridge), Chapter 34 from Book Three, Chapter 2, “Of Faith. The Definition of It. Its Peculiarities.“, Calvin explains how and why the work of the Holy Spirit is necessary for us to receive saving faith.
34. But as Paul argues, “What man knoweth the things of a man, save the spirit of man which is in him? even so the things of God knoweth no man but the Spirit of God,” (1 Cor. 2:11). If in regard to divine truth we hesitate even as to those things which we see with the bodily eye, how can we be firm and steadfast in regard to those divine promises which neither the eye sees nor the mind comprehends? Here human discernment is so defective and lost, that the first step of advancement in the school of Christ is to renounce it (Mt. 11:25; Luke 10:21). Like a veil interposed, it prevents us from beholding divine masteries, which are revealed only to babes. “Flesh and blood” does not reveal them (Mt. 16:17). “The natural man receiveth not the things of the Spirit of God: for they are foolishness unto him; neither can he know them, for they are spiritually discerned,” (I Cor. 2:14). The supplies of the Holy Spirit are therefore necessary, or rather his agency is here the only strength. “For who has known the mind of the Lord? or who has been his counselor?” (Rom. 11:34); but “The Spirit searcheth all things, yea, the deep things of God,” (1 Cor. 2:10). Thus it is that we attain to the mind of Christ: “No man can come to me, except the Father which has sent me draw him: and I will raise him up at the last day.” “Every man therefore that has heard, and learned of the Father, cometh unto me. Not that any man has seen the Father, save he which is of God, he has seen the Father,” (John 6:44, 45, 46). Therefore, as we cannot possibly come to Christ unless drawn by the Spirit, so when we are drawn we are both in mind and spirit exalted far above our own understanding. For the soul, when illumined by him, receives as it were a new eye, enabling it to contemplate heavenly mysteries, by the splendor of which it was previously dazzled. And thus, indeed, it is only when the human intellect is irradiated by the light of the Holy Spirit that it begins to have a taste of those things which pertain to the kingdom of God; previously it was too stupid and senseless to have any relish for them. Hence our Savior, when clearly declaring the mysteries of the kingdom to the two disciples, makes no impression till he opens their minds to understand the Scriptures (Luke 24:27, 45). Hence also, though he had taught the Apostles with his own divine lips, it was still necessary to send the Spirit of truth to instill into their minds the same doctrine which they had heard with their ears. The word is, in regard to those to whom it is preached, like the sun which shines upon all, but is of no use to the blind. In this matter we are all naturally blind; and hence the word cannot penetrate our mind unless the Spirit, that internal teacher, by his enlightening power make an entrance for it.
[emphasis added]
This is only one of many arguments Calvin makes with Scripture as his proof in his Institutes to explain why salvation is entirely the work of God. It is odd to me that salvation, as entirely the work of God, is identified with Calvin, or Augustine, rather than Paul, when it is Paul who wrote:
For it is by grace you have been saved, through faith—and this not from yourselves, it is the gift of God— not by works, so that no one can boast. For we are God’s workmanship, created in Christ Jesus to do good works, which God prepared in advance for us to do.
Praise be to the God and Father of our Lord Jesus Christ, who has blessed us in the heavenly realms with every spiritual blessing in Christ. For he chose us in him before the creation of the world to be holy and blameless in his sight. In love he predestined us to be adopted as his sons through Jesus Christ, in accordance with his pleasure and will— to the praise of his glorious grace, which he has freely given us in the One he loves. In him we have redemption through his blood, the forgiveness of sins, in accordance with the riches of God’s grace that he lavished on us with all wisdom and understanding.
No one can understand why God saves some and others are condemned to die in their sin. We can only testify to the truth as we are commanded to do, and let the Holy Spirit carry out the plan. Nevertheless, it is wrong for anyone, even those who believe, to resist the truth revealed in Scripture because an imperfect human reason and moral sense cannot understand the ways of God, the Creator of the Universe, and his righteousness and justice. As Paul bluntly says:
But who are you, O man, to talk back to God? “Shall what is formed say to him who formed it, ‘Why did you make me like this?’” Does not the potter have the right to make out of the same lump of clay some pottery for noble purposes and some for common use?
We can only bow our heads and humbly acknowledge his glory, thankful that He chose us, and pray for the salvation of those we love, or rather, those who the Spirit leads us to pray for, including those who seem impossible to love.
Oh, the depth of the riches of the wisdom and knowledge of God!
How unsearchable his judgments,
and his paths beyond tracing out!
“Who has known the mind of the Lord?
Or who has been his counselor?”
“Who has ever given to God,
that God should repay him?”
For from him and through him and to him are all things.
To him be the glory forever! Amen.
BETWEEN TWO CITIES 
Thaanks for this
By: Esther Hampton on January 2, 2023
at 7:58 pm