Let's imagine it's currently Wednesday the 1st. Does "next Saturday" mean Saturday the 4th (the next Saturday to occur) or Saturday the 11th (the Saturday of next week)?
It hadn't occured to me that I could be misunderstood, in the same way that it didn't occur to me to explain that Saturday is the one after Friday. When I say "next Saturday" it's completely obvious what I mean!
Judging by the comments here, and the fact that 4/9 people in my group thought I meant one thing and the other 5/9 thought I meant the other thing, this is a phrasing that I'll have to retire. Even my own mother disagrees with me! I don't know how I've made it so far through life without it being a problem before now
Following only works when you are taking about both of them. "We're having pizza this Saturday and tacos the following Saturday." is very clear. If you just say "We're having tacos the following Saturday", there is no context to indicate the saturday following what?