Because they're quicker and better than you'll ever be, because it's literally their job. You see a cupboard full of stuff, you try and work out what you want to keep, does this object belong with that other object, do you need to wrap this, maybe this thing here should go into the box you've got half packed downstairs, will that make it too heavy, is that little jug ok right in the corner of the box maybe you need to pad it out, what can you pad it with, sure there's a cushion somewhere, no not that one, sod it a cardigan will do, what if you want to wear it for work next week, oh is that the little spoon Aurelia made at the half term workshop that time ... this all goes on for hours, days (weeks). The packers meanwhile with their magic 3d minds have everything stripped and safely boxed into manageable loads in 10 minutes.
Surely you've moved house before? And had that terrible experience on the morning of the move when even though you've been surrounded by precarious piles of boxes for three weeks previously and thought that you just had a few last minute things to put away, in reality that meant six hours of feverishly throwing plants, remote controls, shoes, books, pets, children etc into a succession of wrong shaped boxes from Sainsbury's/neighbours' soggy garden sheds and full of dubious stains from the recycling bin like you're in some kind of demented Krypton factor you can't win. How much would you pay to avoid never having to do that again? Now think of the days of packing that preceded that morning. How much is it worth to avoid them?
That, is what you pay packers for.