Why leave headspace when bottling?

If you don't leave any head space you are in danger of the bottle exploding (bottle bomb) because the priming sugar and the yeast will continue to create CO2 to carbonate your beer and without enough head room the bottles will explode because the pressure will need to go somewhere!

Cheers!

Gas compresses under pressure. Liquid doesn't.

If you have no head space, then when CO₂ is produced after bottling, there's nowhere for the pressure to go but to break the bottle.

If you have too much head space, then if enough CO₂ is produced to produce the bottle, then there's quite a bit of compressed gas expanding, and that expansion is dangerous, throwing bits of glass around the place, and perhaps either hurting someone or breaking neighbouring bottles in storage.

I remember a product recall of soft-drinks in New Zealand because the head space was too large, and accidents were occurring in supermarkets.

What I've been told is that the CO2 from that space is what dissolves into the beer to carbonate it. I can tell you from my experience that little to no headspace makes the beer carb less and slower and lots of headspace makes it carb more.