For example, why did the leafs take on Horton’s contract? I’m not arguing at all, I genuinely don’t get how it works.
The Horton thing was about real dollars - his contract wasn't insured, so the Blue Jackets were still paying his salary. With limited resources, it was obviously in their interest to have those dollars going to an actual roster player. For the Leafs, it was an opportunity to move on from Clarkson and "free up" that cap space by turning it into potential LTIR space instead of using in on a useless Clarkson, as they have much lesser concerns re: actual dollars. Every penny of Horton's contract still counted against the cap, but the potential LTIR space gave the Leafs flexibility. It didn't create more space than they would have had without Horton's contract, but it did mean they could essentially re-use those cap dollars on other contracts.
That's probably the easiest way to look at it - it doesn't create additional space, but, rather, it allows space to be used twice. The team's functional cap ceiling remains the same (with some of the complications I mentioned in my previous post).