There is good reason to believe that when the Bible uses the words "all" or "world," it is not referring to every single human being, but rather to one of the following:
For a fuller response, check out Calvinism and "desires all people to be saved" (1 Timothy 2)
God is not the "author" of sin in the sense that God is not the one who commits sin, and God is not guilty of sin.
At the same time, because God is completely sovereign over creation and is metaphysically the ultimate cause of everything, God can be said to be the ultimate "cause" of sin.
This does not make God immoral because the one who commits and is guilty of sin is always the sinner, and not God.
For a fuller response, check out Is God the author of sin? - Gordon Clark's answer.
Some argue that if everyone who is predestined to salvation will definitely be saved, then there is no reason to evangelize.
However, here are two responses:
The context is that the Israelites were saying that God was unjust and would not forgive them even if they repented (verse 2, 19, 25). They were saying that God had "pleasure" in punishing them.
In response, God says that He does not have "pleasure" in punishing the wicked, and that He is completely ready to forgive the wicked if they turn to Him in repentance. God "would rather" that the wicked turn in that God has commanded righteousness, and righteousness is better than wickedness.
There is simply no contradiction between these statements:
In other words, God desires repentance in the sense that He has commanded repentance and will forgive anyone who repents, but God does not desire repentance for some people in the sense that He has not chosen to grant them repentance. There is no contradiction here, and this interpretation is consistent with the rest of Scripture.
In response, God says that He has no "pleasure" in punishing the wicked
Calvinism is fair because people who are punished with hell fully deserve that punishment because of their sin. The fact that their fate was predestined by God does not mean they do not deserve this fate.
The objection that Calvinism is "unfair" uses an arbitrary, foreign definition of "fairness" that the Bible simply does not teach.
When we examine what Scripture teaches concerning God's foreknowledge, we find that God's foreknowledge refers to a "foreloving" of particular people, or a prior commitment to have a special relationship with particular people, rather than to a passive knowledge of what people would do in the future.
For a fuller response, check out God's "Foreknowledge" and Unconditional Election.
Some argue that free will is more glorifying to God because people freely choosing God is more glorifying to God than if God simply predestined people for salvation.
However, this assertion is subjective and arbitrary. We could just as easily say that Calvinism is more glorifying to God because it gives God all of the credit for salvation, and gives sinners greater dependence upon God, greater joy in recognizing that they were saved from utter hopelessness, and greater assurance in their salvation.
That God commands people to "obey," "choose," and "believe" does not necessarily mean that people must have the free will to do these things. It simply means that people should do these things. There is no reason to exclude the possibility that God commands these things, yet people, on their own, are unable to do these things.
There is simply no justification for the assertion that God commanding these things must mean that humans have the free will to do these things.
Rather, the Bible clearly teaches that humans, in their natural sinful state, would never choose God.
For a list of Bible passages that teach that humans, left to themselves, are both unwilling and unable to obey, choose, and believe in God, check out Top 24 Bible Verses about Inability to Turn to God (ESV).
The Arminian view of prevenient grace is simply not taught by Scripture. Rather, Scripture is clear that everyone who is "drawn" or "called" by God definitely will be saved, and that faith is not generated by human free will, but is rather the result of regeneration, or being "born again" by God.
For a fuller response, check out Prevenient Grace - Why the Arminian Definition Fails.
That humans do not have free will apart from God does not mean they are puppets or robots. Humans are completely different from puppets and robots because they have a will that makes meaningful decisions. That our will is not free from God does not make our decisions meaningless.
Our decisions and actions are meaningful, which means they can be rewarded and punished. In contrast, puppets and robots are inanimate objects that do not make meaningful decisions that can be rewarded or punished.
For a fuller response, check out Predestination, Calvinism, Puppets, and Robots - Gordon Clark.
Responsibility does not depend upon free will, but rather upon there being an authority who will judge us for our actions. Whether we are free or not ultimately does not matter. What matters is the answer to this question: "Have we done something that deserves punishment?"
If we argue that it isn't fair for God to punish us for something we don't have the ability to overcome, then we have a false definition of what is "fair." God is the sovereign creator, and because He has decided to punish totally depraved sinners because of their sin, that is fair simply because that is who God is and what God has decided to do.
For a fuller response, check out Predestination, Free Will, and Responsibility - Gordon Clark.
"Your children" and "you" refer to different groups of people. Jesus desires to gather "your children," (His people), but "you" (the Scribes and the Pharisees) were unwilling.
The people who were unwilling were the Scribes and the Pharisees, not the people Jesus desired to gather.
For a fuller response, check out Matthew 23:37
We simply desire to interpret the Bible in a manner that is consistent and non-contradictory, which is necessary for a worldview that does not result in skepticism.
Scripture is extremely clear in teaching the doctrines of Calvinism. The answers to objections that Arminians raise against Calvinism are reasonable and logical.
That you simply do not like the answers does not mean they are illegitimate.