Do you believe those in John 2 who believed in Him were believing on Him for born-again salvation from sin, and He rejected them for this?
Or, was it that they were believing in Him for some ulterior motive, such as the text seems to suggest. He knows what is in man, true. We are all sinners, including them. Their believing on Him could not have been for salvation from sin. All that come to Him, He saves, and they come to Him because they are drawn to Him to be saved, realizing also why they need to be saved.
I don't think this text can say what I think you are trying to make it say: In that some come to Him to be born again, and are thus rejected. I believe other Scriptures teach this to be impossible.
Jesus says in John 10:10 "But you do not believe because you are not of My sheep."
I don't believe Jesus rejects anyone for salvation, when they come to Him for this. I believe you are suggesting otherwise. You never elaborated on what type of faith saves, nor what type of faith was represented in John 2. If you did, it was rather unclear.
The point I think he was making is that faith does not grab the wind by the tail and tell it to blow here.
Jesus said being born again is like the wind that cannot be controlled nor understood.
One does not get saved simply because he trusts Christ. If that were so then he could control the wind.
No, the opposite is the case. One trusts Christ because the "wind" has blown his way and he has been born again.