Joh 15:16 "You did not choose Me, but I chose you and appointed you that you should go and bear fruit, and that your fruit should remain, that whatever you ask the Father in My name He may give you.
Unconditional election unto salvation is read into this verse and not read out of it for it is not there. The Lord Jesus was speaking to His apostles and what did He really say actually?
"I chose you and appointed you that you should go and bear fruit, and that your fruit should remain..."
He did not say that "I chose you to be saved." No! That is twisting and distorting the text! He was talking about fruit-bearing not salvation. This has nothing to do with salvation but all about His choice of them as apostles. All one has to do is to move nine chapters back and it becomes clear:
Joh 6:70 Jesus answered them, "Did I not choose you, the twelve, and one of you is a devil?"
71 He spoke of Judas Iscariot, the son of Simon, for it was he who would betray Him, being one of the twelve.
Judas was one of the chosen ones. He was among the chosen twelve. And yet, was Judas saved? No. Judas was given the awesome privilege to tell others about Him and testify about Him. But he wasted it away, not being truly converted.
With all the privileges that the Lord chose him into, he should have truly repented and make good of the Lord's choice of him.
Israel is a chosen nation. But not all Israelites are saved. They were chosen and given the privilege to witness and tell the nations about the true living God. And yet, many of them neglected their privileged status and even became idolatrous.
Some people who are influenced by Calvin just go on reading this verse carelessly. They just parrot what their favorite Bible teachers say about the text instead of really reading the text in its face value.