What's wrong with Calvinism?​

I'm going to provide a summary of verses in response to the ideas of TULIP.  These might not mean a lot to someone who isn't familiar with Calvinistic (or Reformed Theology) teachings, so I've put a short summary of my understanding in parentheses.  These doctrines aren't all held by everyone who calls themselves a Calvinist, but almost all Calvinists will hold to one or more of these false doctrines.

Total Depravity (Man is so wicked that they can't even trust the gospel.  Most Calvinist doctrines rest on this assumption.).
We have free choice:
  • ¶ And if it seem evil unto you to serve the LORD, choose you this day whom ye will serve; whether the gods which your fathers served that [were] on the other side of the flood, or the gods of the Amorites, in whose land ye dwell: but as for me and my house, we will serve the LORD. (Joshua 24:15)
  • I call heaven and earth to record this day against you, [that] I have set before you life and death, blessing and cursing: therefore choose life, that both thou and thy seed may live: (Deuteronomy 30:19)
  • For if ye turn again unto the LORD, your brethren and your children [shall find] compassion before them that lead them captive, so that they shall come again into this land: for the LORD your God [is] gracious and merciful, and will not turn away [his] face from you, if ye return unto him. (2 Chronicles 30:9)
  • If we confess our sins, he is faithful and just to forgive us [our] sins, and to cleanse us from all unrighteousness. (1 John 1:9)
  • And ye will not come to me, that ye might have life. (John 5:40)
  • And the Spirit and the bride say, Come. And let him that heareth say, Come. And let him that is athirst come. And whosoever will, let him take the water of life freely. (Revelation 22:17)
It's also sometimes said by Calvinists that believing the gospel is a work and that's why we can't have a choice in the matter, but scripture proves this wrong:
  • But to him that worketh not, but believeth on him that justifieth the ungodly, his faith is counted for righteousness. (Romans 4:5) 

Unconditional Election (God picks who goes to heaven and therefore also who goes to hell).
God wants everyone to be saved:
  • ¶ The Lord is not slack concerning his promise, as some men count slackness; but is longsuffering to us-ward, not willing that any should perish, but that all should come to repentance. (2 Peter 3:9)
  • Therefore as by the offence of one [judgment came] upon all men to condemnation; even so by the righteousness of one [the free gift came] upon all men unto justification of life. (Romans 5:18)
  • Who will have all men to be saved, and to come unto the knowledge of the truth. For [there is] one God, and one mediator between God and men, the man Christ Jesus; Who gave himself a ransom for all, to be testified in due time. (1 Timothy 2:4-6)
I also believe that God knows who will be saved by His foreknowledge of everything that will happen (that the elect are those who will freely trust the gospel), and they are those who are predestinated to be saved (something Calvinists tend to disagree with).  It doesn't say He chose who the elect were before we were made:
  • Elect according to the foreknowledge of God the Father, through sanctification of the Spirit, unto obedience and sprinkling of the blood of Jesus Christ: Grace unto you, and peace, be multiplied. (1 Peter 1:2)
Many Calvinists will use this verse to say that God singles people out to be drawn to Jesus:
  • No man can come to me, except the Father which hath sent me draw him: and I will raise him up at the last day. (John 6:44) 
But neglect to include this verse in their point:
  • And I, if I be lifted up from the earth, will draw all [men] unto me. (John 12:32) 

Limited Atonement (Jesus Christ only died for the saints (the "elect"), not for everyone):
He died for everyone:
  • For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life. (John 3:16)
  • For God sent not his Son into the world to condemn the world; but that the world through him might be saved. (John 3:17)
  • But we see Jesus, who was made a little lower than the angels for the suffering of death, crowned with glory and honour; that he by the grace of God should taste death for every man. (Hebrews 2:9)​
  • ¶ But there were false prophets also among the people, even as there shall be false teachers among you, who privily shall bring in damnable heresies, even denying the Lord that bought them, and bring upon themselves swift destruction. (2 Peter 2:1)
  • All we like sheep have gone astray; we have turned every one to his own way; and the LORD hath laid on him the iniquity of us all. (Isaiah 53:6)
You can see that He's the Savior not only to those who believe, but to unbelievers, as well:
  • For therefore we both labour and suffer reproach, because we trust in the living God, who is the Saviour of all men, specially of those that believe. (1 Timothy 4:10)
And as John is surely seen as one of the "elect" by a Calvinist, and he speaks of the propitiation applying to others in this verse, he can't be referring to the "elect" only:
  • And he is the propitiation for our sins: and not for ours only, but also for [the sins of] the whole world. (1 John 2:2)
He must truly be referring to the whole world.

Irresistible Grace (If God chooses to save you, you have no choice in the matter):
It's possible to resist the Holy Ghost:
  • ¶ Ye stiffnecked and uncircumcised in heart and ears, ye do always resist the Holy Ghost: as your fathers [did], so [do] ye. (Acts 7:51)

Perseverance of the Saints (Falsely characterized as the same Once Saved Always Saved that many others believe in.  Says that those who are saved will persevere in faith and good works until the end.  Some say that you won't ever have doubts about your salvation, as well.):
It's possible to be a "carnal Christian" or someone whose life doesn't outwardly reflect they're saved:
  • ¶ And beside this, giving all diligence, add to your faith virtue; and to virtue knowledge; And to knowledge temperance; and to temperance patience; and to patience godliness; And to godliness brotherly kindness; and to brotherly kindness charity. For if these things be in you, and abound, they make [you that ye shall] neither [be] barren nor unfruitful in the knowledge of our Lord Jesus Christ. But he that lacketh these things is blind, and cannot see afar off, and hath forgotten that he was purged from his old sins. (2 Peter 1:5-9)
And it's possible to doubt, even as John the Baptist did:
  • ¶ The next day John seeth Jesus coming unto him, and saith, Behold the Lamb of God, which taketh away the sin of the world. (John 1:29)
  • And said unto him, Art thou he that should come, or do we look for another? (Matthew 11:3)
  • ¶ And John calling [unto him] two of his disciples sent [them] to Jesus, saying, Art thou he that should come? or look we for another? (Luke 7:19)