NB: This is mildly in jest, but also not really.
Their second strong point is the fact that they have valuable data hidden in their social graph.
Automating a browser to unfollow companies basically undermines both of their valuable assets, so they are not interested in making this process seamless.
Good thing they are hit with lawsuits that make it a precedent to allow them to be scraped.
- go to your follow list (manually, via Chrome or whatever browser you are using)
- execute your unfollow script in the dev console (so, yes, it must be rewritten in JS)
- go to your next follow list page (or refresh the page, or scroll down... I don't actually know how the follow list page looks like in linkedin)
- have some patience and you'll end up unfollowing everyone on linkedin
It's what I call pseudo-scraping: yes, there is some automation (the JS script) but it requires manual intervention (manual scroll down, clicking next page, etc.). So far, it has always worked for me.
Once you know, you'd be smart to no longer trust them, no matter how enticing.
I deleted my account years ago, nullrouted their email, and haven't looked back since.