My friend doesn't seem to get the concept of "Runes are essential"

How do I explain it to him?

1v1 him with the same champ as him while you have a rune page and he doesn't.
Enjoy the stomping, my friend did this to me - he had double my MR at level 5 (Mordekaiser) and annihilated me. I then started buying runes.

depending on the setup you use you can walk out of the fountain with like 1k gold worth of effectively free stats for earlygame.

1v1 him with ~1k health level 1 GP.

Tell him that roughly, runes yield something like 1k gold worth of stats from the get go.
Some more some less, some are harder to quantify.

If you went all AD/lvl runes you would be getting something like 1800gold worth of AD (50AD), for example, or if you went all flat AD, you'd have +22AD at lvl1 (roughly 800gold worth, give or take).

well yeah they are.

If youre going out into the wild make sure you bring a law rune and a few wind runes so you can teleport out in case you run into a problem

Show him what its like to spawn with both parts of your passive up on akali.

"Hey friend, runes are essential."