We need to have a clear understanding of what the gospel is. It is unhelpful to define it so broadly such that all theological truth is the gospel. Every moral is theological, but the command not to murder is not the gospel.
Gospel (noun: ευαγγελιον, euangelion; verb: ευαγγελιζο, euangelizo) means "good news". The word appears over 100 times in the New Testament. Scripturally the word is linked to Jesus; specifically that man can be reconciled to God thru him. In various places the meaning is expanded as can be expected from a word that means "good news". Good news can be about many things; in Scripture we apply this to the news about Jesus' salvation. Gospel is variously attached to Jesus, and the kingdom of God, and other concepts. Paul frequently speaks of preaching the gospel and he tells us what the gospel is,
Now I would remind you, brothers, of the gospel I preached to you, which you received, in which you stand, and by which you are being saved, if you hold fast to the word I preached to you—unless you believed in vain.Of first importance is that Jesus:
For I delivered to you as of first importance what I also received: that Christ died for our sins in accordance with the Scriptures, that he was buried, that he was raised on the third day in accordance with the Scriptures, (1 Corinthians 15:1-4)
- died for our sins
- was buried
- was raised on the third day
If you confess with your mouth that Jesus is Lord and believe in your heart that God raised him from the dead, you will be saved. For with the heart one believes and is justified, and with the mouth one confesses and is saved. (Romans 10:9-10)In the first passage we learn that Jesus died for our sins, but little about how his death is for us. Then that Jesus was resurrected from the dead, but little about the nature of his resurrection or resurrection body. In the second passage we learn we must consider Jesus Lord, but how that fits with our concept of the trinity is not expanded. Then that we must believe that he was indeed resurrected.
Now perhaps Paul expounded on this more when he first preached the gospel to the Corinthians, he was after all reminding them of what he previously said. Nevertheless, the core of the gospel is quite simple. Expounding the nature of faith and salvation and atonement is more complex, and we are to move on to the meat from the milk, yet the core of the gospel is that God offers salvation thru Jesus.
If this is the true gospel what is the false gospel? A false gospel is offering salvation thru other means. Offering salvation thru someone other than Christ, or adding requirements that are not required, specifically trying to earn salvation. Peter states,
And there is salvation in no one else, for there is no other name under heaven given among men by which we must be saved.” (Acts 4:12)John adds,
Who is the liar but he who denies that Jesus is the Christ? This is the antichrist, he who denies the Father and the Son. No one who denies the Son has the Father. Whoever confesses the Son has the Father also. (1 John 2:22-23)Salvation is only offered thru Jesus. It is belief in his resurrection and confession of his lordship that brings salvation from God.
Elsewhere Paul denounces the Judaisers for adding requirements to the gospel,
I am astonished that you are so quickly deserting him who called you in the grace of Christ and are turning to a different gospel—not that there is another one, but there are some who trouble you and want to distort the gospel of Christ. But even if we or an angel from heaven should preach to you a gospel contrary to the one we preached to you, let him be accursed. As we have said before, so now I say again: If anyone is preaching to you a gospel contrary to the one you received, let him be accursed. (Galatians 1:6-9)He describes how the circumcision party, whom he calls false brothers, had influenced even Peter therefore Paul rebuked him. What was the false gospel? Justification by works.
Yet we know that a person is not justified by works of the law but through faith in Jesus Christ, so we also have believed in Christ Jesus, in order to be justified by faith in Christ and not by works of the law, because by works of the law no one will be justified. (Galatians 2:16)The true gospel is faith in Christ. The false gospel is trying to earn salvation. Of course God has works for us to do, and we are to work out our salvation with fear and trembling (Php 2:12) in obedience to Christ.
So does Arminianism require that man earn his salvation? No. The charge is false.
Arminianism believes that salvation comes thru Christ alone. God saves man thru Jesus. In order to be saved one must confess that Jesus is Lord and believe in his resurrection. It is thru faith by which we are saved, not works.
Of course Arminiansim holds to the concept that man has the ability to reject God's offer of salvation. And also that faith is a choice to trust in God, something man expresses and God commends him for, though God is always helping man in his frailty and keeping him safe from the enemy who would assail him. So part of the Arminian/ Calvinist debate is whether such faith is something man can have, or something given to man entirely from God. Calvinists would label such Arminian faith a work. This is unjustified, but even if such faith was a "work", it is not a work in the sense Paul is condemning. Paul condemns work that tries to earn. A person expressing faith is not an activity that is similar to activities that try to earn salvation. The Arminian concept of faith is not a work one does like getting circumcised, or tithing. Arminianism and Calvinism both preach salvation thru faith in Christ.
If we assume that Calvinism is true (for the sake of the argument), Arminianism is bad theology or heterodoxy. If would be a stretch to call it heretical. If it is false teaching it should be opposed. But to call it a false gospel is slander. I think Calvinism is a serious error, but is it hardly a false gospel. Arminians are children of God. They preach a true gospel as do Calvinists. They call people to turn from their sins, to trust in Jesus who died for their sins, to follow Jesus who was raised from the dead, to commit to his Lordship in their lives and over this world.
To say that Arminianism is a false gospel is to slander God's children. Something that deeply offends God. God rebuked Job's friends for their false accusations and he continues to defend his people against those who falsely accuse them.