v1-4 - The reason that Paul is so concerned with the behavior of the Corinthian church is because as their pastor, he has an obligation to present them as a pure people to Christ. Yet when heresy comes along, they "put up with it easily enough (v4)."
Paul talks about a "Jesus other than the Jesus we preached" and a "different Spirit." But what does this mean?
From the very beginning of the Church, the message of the gospel has been under attack.
At times it's been a 'Jesus+' message, meaning that it was well and good to believe in Jesus, but you needed to add your own good works to the equation to earn salvation.
Other times Jesus gets reduced to the missing ingredient to a healthy, wealthy, fulfilling life, as in 'be like Jesus in order to enjoy your best life now.'
One of the most pernicious distortions the church is being attacked with now is that Jesus loves you so much that He would never condemn your lifestyle as being sinful or wrong.
The message of this chapter is clear: do not put up with these dangerous, salvation robbing deceptions.
v5-15 - Paul contrasts his own humble approach with that of these deceivers. He concludes that it makes since that those preaching a different gospel look so slick and polished, because they're following the pattern set by the master deceiver, Satan himself.
We tend to think of Satan looking like a hideous monster, but he's not. He "masquerades as an angel of light," as one who often looks very attractive.
This means that often those who look the best outwardly (as judged by the standards of this world) may very well be one sent to try and pull you away from the gospel.