Actually, spiders can stick to their own webs.
First of all, not all spiders weave sticky webs, so right from the start some of them will not stick to their webs because, well, their webs are not sticky.
Secondly, even if the web is sticky, most of the time not all parts of the web are actually sticky, or equally sticky. Depending on the species, various parts of the web can be constructed using different types of silk.
You could thus have parts of the web, like the frames or the spokes, that are not actually sticky, and other parts of the web, most likely the spirals and intersection nodes, that are indeed sticky.
This gives the spider the advantage of actually knowing where the sticky parts are.
Moreover, many spiders are actually very, very tidy, meaning that they keep their legs as clean as possible. This, in addition to the fact that they have hairy legs, helps reduce the chances of getting stuck in the web.
Most spiders walk differently on their web than they do on hard surfaces. Here's a cool example of how the European garden spider walks on its web
So, as a conclusion, spiders can actually stick to their webs, meaning that there's no chemical reason for why they don't actually do so.
The fact that they can easily avoid sticky sections and that they use special techniques when moving around on their webs makes them very, very likely not to get stuck in their own webs.