Ok, well first off, hunting spiders are a thing, so arachnids can be effective predators without webs. Let's suppose that hunting spiders evolved first and web spinning came later (I have no actual knowledge of spider evolution, but let's go with it).

So what do those hunting spiders use web for? I believe they use them to make those fuzzy egg sacks or nests, so protective structures in general. I could totally see that evolving first, the ability to make silk for building nests. Actually many different species have evolved something like that, using excretions to aid in nest building, birds, ants, fish, caterpillars, other insects, it's actually a relatively common trait to develop. Nests are good for hiding, protection from the elements and thermal insulation, a home is nice to have!

I could see it become beneficial if some spiders then developed sticky nests, sometimes bugs might wander in and get stuck, free meal. And then after that, some might develop larger nests, the greater the area of this sticky nest, the more effective it is. And that basically gets us to modern ~~sliders~~ spiders.