As I understand it, not all the strands are sticky. The spider sticks to the ones that are not sticky. I think it is the ones going out from the centre like spokes that are not sticky.
To be more accurate:
"Spiders secrete a substance from the tips of their legs that acts as a
lubricant and counteracts the adhesive nature of the silk proteins."
In other words...
Spiders have special glands in their feet that keep them moist, so
they do not stick to the webbing.
It has a specially designed hook at the end of its' legs that alow it to traverse the web without getting stuck to it. Try the web-site that deals with Garden Spiders for a proper run-down. It is sooooo clever and a real eye opener as to how special they are.........rut.