How do you talk about Jesus without sounding argumentative?

The way to avoid sounding argumentative is to express concern for the other person's soul. People can tell the difference between whether your words are just the presentation of an opposing argument in a debate and whether or not you genuinely care for them and the eternal state of their souls.

For example, you may go to John 14:6 and say, if sharing with your brother, "Your soul may hang in the balance here, because Jesus just said, 'I am the way, the truth, and the life. Nobody comes to the Father but by me.' And frankly, I want to go to the Father with you, not without you."

Not sounding argumentative will happen if we are pursuing the other person's good and they manifestly see that we're concerned for their soul.