You are incorrect. that is an apologetic axiom. In the many years of dealing with the cults on another site, no one proved me wrong on that statement.
For example, you cited John 3:16 as being "out of context" It is not. So I ask you if you know the meaning of the word
context and then supply a reason why it is out of context?
John 3:
13 No one has ascended into heaven except he who descended from heaven, the Son of Man.
14 And as Moses lifted up the serpent in the wilderness, so must the Son of Man be lifted up,
15 that whoever believes in him may have eternal life.
For God So Loved the World
16 “For God so loved the world, that he gave his only Son, that whoever believes in him should not perish but have eternal life.
17 For God did not send his Son into the world to condemn the world, but in order that the world might be saved through him.
18 Whoever believes in him is not condemned, but whoever does not believe is condemned already, because he has not believed in the name of the only Son of God.
ESV
It really is simple: Jesus is talking about salvation of individuals, the reason and reward of salvation, and the state of those who do not do as Jesus said.
The entire pericope is about salvation.