When you say John 3:16 proves that the Calvinists aren’t correct, how do we know it doesn’t prove that they are? Their whole idea is that God makes people believe, right? And John 3:16 says whosoever believes has everlasting life. Do you see what I mean?
I understand what you’re saying but that interpretation is not consistent with John’s choice of words, which imply that anyone can make the choice to believe and receive eternal life. The Greek word translated whosoever in John 3:16 literally means each, every, any, all, the whole, everyone, and is most often translated all. This is consistent with other statements on salvation, such as Matt. 7:7-8, Romans 10:13, 1 Tim.2 3-4, 2 Peter 3:9.
Saying that everyone can believe when you know that in truth only those you’ve pre-selected can believe would be misleading, to say the least. It would be a violation of God’s character and would cast doubt on everything else He said. It would also make it impossible for Him to condemn those who don’t believe.