All that the Father gives me will come to me, and whoever comes to me I will never cast out.
When Jesus says “I will never cast out”, he uses a double negative. If you want to be fancy (and why wouldn’t you?), it’s οὐ μή ἐκβάλω ἔξω: something like “Not not I will cast out.” In English this is bad grammar; in Greek it’s for emphasis. (Also in Czech, for what that’s worth.) In fact, it’s pretty much the strongest negation available in Greek.
The English phrasing I like the most for this idea is at the end of the hymn “How Firm A Foundation”:
The soul that on Jesus hath leaned for repose
I will not, I will not desert to its foes!
That soul, though all hell should endeavor to shake,
I’ll never, no never, no never forsake.
That’s what Jesus is saying here. He will never, no never, no never cast out the one who comes to him in faith. There is no circumstance under which he will reject those who trust in him. I’m not saved by how well I hold onto Jesus– not so well!– but by how well Jesus holds onto me. And he is, as my daughter’s name means, “God of the oath”– the One who always keeps his promises.
So when I’m at my worst, selfish and self-absorbed, seeking my own little kingdom at the expense of everyone else, there Jesus is: holding onto me. Not casting me out. That’s very good news.