*picks teeth* As a matter of fact I linked three in that reblog which itself contains the same proofs in pathsofpassion's rebuttal to the fallacy-riddled, error-stricken OP.
You don’t really need a long drawn-out thing to explain it, though. It’s simple.
- A large portion of the episode goes to showing a huge disparity between the brothers’ priorities. The tension between them increases: Dean thought they were supposed to be a team, a duo to the bitter end and back, while Sam only ever wanted out.
- Sam appears in Dean’s Heaven only as his younger self contemporary to the memory, where the real Sam and Dean always appear as their adult selves even while filling roles from their early lives.
- They have to use the Axis Mundi to travel from Dean’s part of Heaven to Sam’s, and from Sam’s part to Ash’s, but do NOT need to use it to travel from one part of Sam’s Heaven to another.
- Ash says that soulmates’ Heavens are shared – as in, the souls do no have to use the Axis Mundi, the road between sections of Heaven.
Winchesters’ Heavens are not shared
soulmates’ Heaven is shared
therefore Winchesters are not soulmates
I’ve seen a number of people mewling about “well what was the point in mentioning it?!” and it just…it’s like listening to someone come out of watching Fight Club absolutely convinced that Narrator and Tyler Durden were physically separate people. The point of Ash mentioning it was to highlight the exact same rift that the half-hour preceding it had been illustrating. It’s an answer to this exchange:
DEAN: I mean, we’re supposed to be a team. It’s supposed to be you and me against the world, right?
SAM: Dean, it is!
DEAN: (after a pause) Is it?
And the answer is no. If the Winchester boys were “meant to be” as a duo all the way, they would share a Heaven, but they’re not, and they don’t. That is the entire point of the episode: that they’re NOT on the same page, they DON’T have the same priorities, they DON’T have the same goals, they DON’T have a ~mystical bond~.
It also has the elements of the old Mistaken For Gay trope in that Ash found Sam and Dean together, so he probably assumed that they’d been in the same Heaven all along, but he was not there to see the fact that they had to use the Axis Mundi to find each other before that. This is called dramatic irony and serves to highlight the opposite of what’s being stated; ie, Ash talking about soulmates highlights the fact that we just got shown that the Winchesters do not qualify for the description. Hence the uncomfortable looks.
As a footnote, pretty sure you don’t have to abjectly fail at basic algebra to ‘ship Wincest anyway. Just sayin’.