[This is especially true of explanations given by those who oppose Calvinism. It is easier to knock down a straw man than it is to knock down a real man, and so it is easier to criticize an oversimplified Calvinism that the more robust form.]
Some of those who teach the “five points” leave out some of the quotes below:
This death of God's Son is the only and entirely complete sacrifice and satisfaction for sins; it is of infinite value and worth, more than sufficient to atone for the sins of the whole world… This death is of such great value and worth for the reason that the person who suffered it is--as was necessary to be our Savior--not only a true and perfectly holy man, but also the only begotten Son of God, of the same eternal and infinite essence with the Father and the Holy Spirit. Another reason is that this death was accompanied by the experience of God's anger and curse, which we by our sins had fully deserved… Moreover, it is the promise of the gospel that whoever believes in Christ crucified shall not perish but have eternal life… all who are called through the gospel are called seriously.
There is nothing lacking in the payment Christ made for sin. Therefore, when a person tells you that you can be assured of heaven if you repent of your sins and have faith in Christ, he is making a real offer on God’s behalf. There is nothing outside you that keeps you from repenting. If you turn from your sins and trust Christ’s sacrifice to pay for them, you can be saved (John 3:16). It is, in this sense, your choice, and it is a real choice.
This promise, together with the command to repent and believe, ought to be announced and declared without differentiation or discrimination to all nations and people, to whom God in his good pleasure sends the gospel.We do not look for evidence of seeking or evidence of a changed heart before we share the gospel. Everywhere we go we should share the good news of the kingdom (Mathew 28:18-20), and we should make special trips to as many places as possible (Acts 1:8).
…many who have been called through the gospel do not repent or believe in Christ but perish in unbelief is not because the sacrifice of Christ offered on the cross is deficient or insufficient, but because they themselves are at fault…But all who genuinely believe and are delivered and saved by Christ's death from their sins and from destruction receive this favor solely from God's grace--which he owes to no one--given to them in Christ from eternity… Therefore, all people are conceived in sin and are born children of wrath, unfit for any saving good, inclined to evil, dead in their sins, and slaves to sin; without the grace of the regenerating Holy Spirit they are neither willing nor able to return to God, to reform their distorted nature, or even to dispose themselves to such reform…There is, to be sure, a certain light of nature remaining in man after the fall, by virtue of which he retains some notions about God, natural things, and the difference between what is moral and immoral, and demonstrates a certain eagerness for virtue and for good outward behavior. But this light of nature is far from enabling man to come to a saving knowledge of God and conversion to him--so far, in fact, that man does not use it rightly even in matters of nature and society. Instead, in various ways he completely distorts this light, whatever its precise character, and suppresses it in unrighteousness. In doing so he renders himself without excuse before God.God elects, but men are responsible. All of us would reject God’s command to repent and believe if God did not do a special work in our hearts. We need new hearts to repent, but when we do not repent, we are doing exactly what we want to do. We do what we want to do, and we are responsible for our choice.
What, therefore, neither the light of nature nor the law can do, God accomplishes by the power of the Holy Spirit, through the Word or the ministry of reconciliation. This is the gospel about the Messiah, through which it has pleased God to save believers, in both the Old and the New Testament.God’s saves the elect through the preaching of the word (Romans 10:14-15). The Holy Spirit does not act to give men new hearts without this preaching.
In this life believers cannot fully understand the way [God’s giving of a new heart] occurs… this divine grace of [God’s giving of a new heart] does not act in people as if they were blocks and stones; nor does it abolish the will and its properties or coerce a reluctant will by force, but spiritually revives, heals, reforms, and--in a manner at once pleasing and powerful--bends it back.The Canons of Dort allow for a doctrine of persuasive action. God does in some sense persuade men to embrace the truth. God does not coerce the will from outside a person. How this is done cannot be fully understood in this life.
...a ready and sincere obedience of the Spirit now begins to prevail where before the rebellion and resistance of the flesh were completely dominant. It is in this that the true and spiritual restoration and freedom of our will consists. Thus, if the marvelous Maker of every good thing were not dealing with us, man would have no hope of getting up from his fall by his free choice, by which he plunged himself into ruin when still standing upright.God gives some people a new heart. Those people repent of their sins and believe the gospel. Those people also do good works as naturally as sparks fly upward. They are not perfect, but there is a change of heart that results in a new, better life (James 2:14-26).
This is not an exhaustive list of the finer points of the Synod of Dort, but it is a start. I encourage you to study and approve this great statement of faith.
The five points of Calvinism communicate truth, but that truth is incomplete without a careful explanation. All who discuss Calvinism, friend and foe alike, should remember this.