Although the Bible was mostly written down by human authors, it is basic Christian doctrine that its ultimate Author is God. We are told in 2 Timothy 3:16-17 that all Scripture is "theopneustos" (that is, "God breathed", or inspired by God). We are told in 2 Peter 1:20-21 that no prophecy of Scripture comes from one's private interpretation, but rather, God's messengers wrote as the Holy Spirit guided them. These are only the most obvious references to the inspiration of Scripture.
This simple fact should be enough to tell us that the entire Trinity is behind every word of Scripture. We know that the Godhead is not divided. There are no rogue agents in the Trinity. Indeed, God cannot deny Himself (2 Timothy 2:13). But God doesn't just leave us to assume as much. Rather, He tells us plainly that this all comes from the same source.
To begin with, Jesus makes it quite clear that He submits to His Father. In John 12:49, for example, Jesus says "For I have not spoken on My own authority; but the Father who sent Me gave Me a command, what I should say and what I should speak." Therefore, every word we hear Jesus say, we know He got from the Father.
This is later followed by certain promises about the role of the Holy Spirit in the Church, and in particular among the Disciples. In describing the Holy Spirit, Jesus says "However, when He, the Spirit of truth, has come, He will guide you into all truth; for He will not speak on His own authority, but whatever He hears He will speak; and He will tell you things to come. He will glorify Me, for He will take of what is Mine and declare it to you. All things that the Father has are Mine. Therefore I said that He will take of Mine and declare it to you."
Thus, we see that just as the Son gets all His words from the Father, the Holy Spirit gets all His words from the Son (and thus, ultimately, from the Father). The Godhead, therefore, speaks of one accord. There is nothing you can hear from one person of the Godhead that you cannot receive as from God entirely.
This must be kept in mind when we read Scripture, which, again, comes from God. With that in mind, let us consider the prayer of Jesus in the garden of Gethsemane. "Then Jesus came with them to a place called Gethsemane, and said to the disciples, “Sit here while I go and pray over there.” And He took with Him Peter and the two sons of Zebedee, and He began to be sorrowful and deeply distressed. Then He said to them, “My soul is exceedingly sorrowful, even to death. Stay here and watch with Me.” He went a little farther and fell on His face, and prayed, saying, “O My Father, if it is possible, let this cup pass from Me; nevertheless, not as I will, but as You will.” Then He came to the disciples and found them sleeping, and said to Peter, “What! Could you not watch with Me one hour? Watch and pray, lest you enter into temptation. The spirit indeed is willing, but the flesh is weak.” Again, a second time, He went away and prayed, saying, “O My Father, if this cup cannot pass away from Me unless I drink it, Your will be done.”" (Matthew 26:36-42).
This passage is as instructive as it is descriptive. We've all seen the bumper sticker. "What Would Jesus Do?" Jesus would pray. And when He prayed, He would pray according to the "formula" He, Himself, gave earlier in the same Gospel: "In this manner, therefore, pray: Our Father in heaven, Hallowed be Your name. Your kingdom come. Your will be done On earth as it is in heaven." (Matthew 6:9-10, emphasis mine). For the Christian, the will of God is vitally important. In fact, nothing should be ranked higher. Thus, when we pray, we should also pray according to the will of God.
Matthew 6:9-13 is not the only place in Scripture that gives instructions on prayer. In 1 Timothy 2:1-4, we read "Therefore I exhort first of all that supplications, prayers, intercessions, and giving of thanks be made for all men, for kings and all who are in authority, that we may lead a quiet and peaceable life in all godliness and reverence. For this is good and acceptable in the sight of God our Savior, who desires all men to be saved and to come to the knowledge of the truth."
It is clear, lacking certain theological biases, that God wants us to pray for all men, and particularly for those who are in authority, because He desires all men to be saved and come to the knowledge of the truth. This would seem to be fairly simple. Do I pray for Rishi Sunak? Yes, because God desires all men to be saved and come to the knowledge of the truth. Do I pray for Joe Biden? Yes, because God desires all men to be saved and come to the knowledge of the truth. Do I pray for Vladimir Putin? Yes, because God desires all men to be saved and come to the knowledge of the truth.
But as simple as that is, man has a nasty habit of complicating the uncomplicated. Like earbuds in a pocket, when we run Scripture through our traditions, it comes out scrambled. Enter Calvinism, a man-made philosophy that suggests God only wants all kinds of men to be saved.
But there's a problem. If this passage is only supposed to be interpreted in an extremely limited sense, that means it must be interpreted in the opposite way to other prayer instructions. See, on the one hand, you could suggest just not praying for a man unless you're 100% sure God wants that particular individual saved. But that involves making judgement calls you have no business making (unless, of course, you go back to the more logical interpretation and just say yes, God wants all men saved). Thus, you are left with one option: Lump "your will be done". God tells us to pray for all men, so we should pray for them regardless of God's will!
And Paul, according to the Calvinist interpretation, did just that. In Romans 9:1-5, ironically the beginning of a passage Calvinists love to cite as though it were some kind of trump card, we read "I tell the truth in Christ, I am not lying, my conscience also bearing me witness in the Holy Spirit, that I have great sorrow and continual grief in my heart. For I could wish that I myself were accursed from Christ for my brethren, my countrymen according to the flesh, who are Israelites, to whom pertain the adoption, the glory, the covenants, the giving of the law, the service of God, and the promises; of whom are the fathers and from whom, according to the flesh, Christ came, who is over all, the eternally blessed God. Amen."
Israel, from the time of Christ until this very day, has rebelled against Christ, damning many of them. In fact, those who believe are often referred to in Scripture as "the remnant", there are such a small portion of them. Yet, Paul, of course inspired by the Holy Spirit, expresses such a desire for their salvation that he effectively says he would swap. He would go to Hell if it meant his countrymen, the majority of whom would in reality perish, would instead receive eternal life.
But it's not even just Paul! Christ Himself declares "“O Jerusalem, Jerusalem, the one who kills the prophets and stones those who are sent to her! How often I wanted to gather your children together, as a hen gathers her chicks under her wings, but you were not willing!" (Matthew 23:37). Who was not willing? God? No, this is God Himself saying "I wanted to". But you, Jerusalem, were not willing. And that's why God did not do what He wanted to do.
So let's go back a bit. Jesus, being God, wants to do something. And Jesus, in His particular role in the Godhead, can neither say, nor do, anything but what the Father says or does (John 5:19). And of course, the Holy Spirit is beholden to both of them, so He's fully consenting to this. This is what God wanted. But it's not what the Jews wanted.
"So what, God was thwarted?" a Calvinist might ask. Well, we'll come back to that in a moment, but first, let me ask, if God says something, who can disagree? Realistically, it is possible, but utterly immoral, to disagree with God. In fact, when Peter took Him aside and rebuked Him, His response was "Get behind Me, Satan! You are an offense to Me, for you are not mindful of the things of God, but the things of men." (Matthew 16:23). So, when we don't understand what God says, it's better to just say "I don't understand" than to use that not understanding of disagreement. If you don't understand how Jesus can say "I wanted to gather your children" but "you were not willing", well, too bad, Jesus was willing, but Jerusalem weren't.
But it actually is relatively easy to understand how this could be, especially when we consider what else Scripture reveals about God. See, as previously mentioned, God cannot deny Himself (2 Timothy 2:13). That is, He is a logical being. Not even He can have His cake and eat it too. Thus, just like with us, it is possible for Him to have more than one conflicting desire.
The obvious example is the prayer of Christ we looked at earlier. He wanted the cup to pass from Him, "...nevertheless, not as I will, but as You will." Well how can Jesus, being God, say not as I will, but as You will, unless God has two conflicting wills? We can safely assume that Jesus was no masochist, nor was His Father a sadist. God was not pleased by the cross because it was an enjoyable experience. He was pleased because it served a greater purpose! By doing what He didn't want to do, He achieved what He did want to achieve.
Ultimately, even if this explanation was insufficient, it is essential for us, as Christians, to let Scripture be Scripture. Therefore, since Scripture quite clearly tells us that God is willing for all men to be saved and come to the knowledge of the truth, yet makes it clear that we are not always willing, and this is why we lose out on salvation (whereas He still achieves His goal: Believers are saved), we have no option but to believe Him. After all, when you find yourself in conflict with the word of the Father, the Son, and the Holy Spirit, what benefit do you have over Peter when he said "Far be it from You, Lord; this shall not happen to You!"? I therefore submit that with one accord, the Holy Trinity rejects Calvinism, and thus, as His people, so should we.