Verse 3 is a diagnostic. You know, like the mechanic at the dealership hooks your car up to a machine and runs diagnostics to see what's wrong. Well, this is a diagnostic, and here it is. If someone is spreading wrong ideas and they won't agree to the words of Jesus and they won't agree with other godly teaching. . . That's three things, quite a lot, so we're not talking about people who are simply wrong, but rather people who are wrong and cannot be persuaded even by Jesus himself. They are stuck in their wrong-headedness and really proud of it. The first part of verse 4 completes that thought. This person is conceited and understands nothing.
We shouldn't read the word "conceited" here as some kind of hate word. We say something like "he's so conceited," and we basically mean that he's the devil, I hate him, and so on, but that's not what Paul, or the Holy Spirit through Paul, is saying here. He's saying this person is so full of his own thoughts and ideas that there's no room for God's ideas.
Each one of us has been at this point at least once in our lives. When, in our minds and from our perspective, our ideas got bigger than God's ideas. You want an example of this? Look at Acts 10. Peter has a vision of this huge sheet coming down with different animals on it, and a voice says, "Kill and eat."
Peter had been a Jew before he knew Jesus, and the Jews have some strict dietary laws. This stuff on the sheet was against the law for Jews, what Peter had been, and so Peter says, "No way. I have never eaten anything unclean!" Which is what that kind of food was called by the Jews.
The voice from heaven says, "Don't call anything unclean that God has made clean." The Bible says this happened a total of three times.
Do you see how Peter had his head full of his own idea? And God kept telling him, "Don't call this stuff unclean because I've made it clean." Or, ineffect, "Peter, you're wrong and I'm right. Now wise up."
And amazingly, Peter still argues. He's not a bad guy, he's just conceited. That's conceit in it's simplest, least mean-spirited state. It's how most of us get conceited.