Because he didn't tie it.

Because he's not the one who tied it.

In my mind I denote the two brothers as "the nice one" and "the smart one".

• Nice one = "Alfred" = the one who loved Sarah
• Smart one = "Freddie" = the one who loved Scarlett Johansson

Freddie operates as the "ingenieur" of the pair. He's aggressive and pugnacious. He's the one who wants to tie the Langford Double; he pushes back against Angier with, "Oh you think you know knots better than me? Do ya?" And he's the one who ties Julia's arms the night she dies.

Alfred is the one with enough empathy to go to the funeral. Angier asks him which knot he tied: he doesn't know. He really doesn't! He didn't tie it.

Alfred and Freddie have had arguments & shouting matches about what happened that night. Freddie insists that he tied the simple slip knot; Alfred doesn't believe him. So that's an assumption on my part. No such scene is ever shown. But it would explain why Alfred doesn't know. And that inference leads me to believe two things.

One: at least part of the diary is genuine. Angier reads it and observes Borden's "divided mind": that suggests both men taking turns writing in the diary. I think Borden took an existing diary, and either EXTENDED it with fake entries up to the point where Scarlett "steals" it; or re-copied it over with the Tesla cipher and fake entries toward the end. Creating a diary from scratch would take a lot of work: easier to use existing entries.
(By the way, if part of the diary is genuine, then Borden is exposing his "divided mind" to Angier, betting that he won't understand the secret.)

Two: Alfred thinks Freddie is a liar. He insists to Alfred that he tied the simple slip, and Alfred doesn't believe him.

And he's right, isn't he? No one knows Freddie better than Alfred. From what we see of Freddie, he's arrogant and dismissive and belligerent; kind of an asshole. Thinks he knows everything. He initially bonds with Scarlett over her anger at Angier and cynical assessment of him: qualities that speak to Freddie.

When Borden ties the knot on Juiia the night she drowns, that significant glance between them sure as hell implies that he ties the Langford Double. (The fact that she wasn't able to untie it is itself pretty convincing.) So, I guess I'm saying I also think Freddie is a liar.

So Angier goes to Borden's magic show. Alfred is performing that night. Angier holds the gun on him: he still doesn't know, doesn't have any better answer for Angier. So Angier shoots him. This is kind of a cruel irony: the one who didn't do it is shot as punishment. But that means Freddie has to bite down on the stick and take the maiming in cold blood (it's Freddie whose fingers are "still bleeding").

Nazgul's answer here about who's who is right on the money, as I see it, though I differ with him in that I think the twins discussed it a lot. Fought about it. Nazgul also observes that Freddie is less mature than Alfred, and I think that's important. Freddie ties the Langford; Alfred gets shot in consequence. Freddie starts the affair with Scarlett; Alfred loses his wife in consequence.** Freddie is the one who can't leave Angier alone, and goes below stage at the final performance – but this time Freddie suffers the consequence, gets hanged.

(Which of them gets buried in the coffin?? I initially thought Alfred. But Freddie is the one acting like an asshole at dinner, ordering the champagne and being obnoxious: and if they just had a performance, then they just switched, which would mean that Freddie had been Fallon. If Freddie was in the coffin, that dilutes my idea somewhat, about the one twin starting shit and the other bearing the consequences.)

So anyway: that's it. The smart one tied the knot; the nice one faced the questions. Offscreen they had many an argument about it, going over the events again and again. The smart one always insisted he tied the right knot, the simple slip. The nice one never believed him.

• I realize that the way I wrote that sentence minimizes Sarah. As if it's more important that Alfred loses someone than it is that Sarah dies. That's not my view: I'm just going for the parallel sentence construction here, for this point about Freddie as compared with Alfred.

Because he didn't tie it.

With Borden, there's "the nice one" and "the smart one":

• "Alfred" = the nice one = the one who loved Sarah
• "Freddie" = the smart one = the one who loved Scarlett Johansson

Freddie operates as the "ingenieur" of the pair. He's aggressive and pugnacious. He's the one who wants to tie the Langford Double; he's the one who gets argumentative with Angier, saying "Oh you think you know knots better than me? Do ya?" And he's the one who ties Julia's arms the night she dies.

Alfred is the one with enough empathy to go to the funeral. Angier asks him which knot he tied. Alfred says he doesn't know. He really doesn't! He's not the one who tied it.

This tells us so much about the two brothers. Remember Alfred says "I've asked myself that question a thousand times." When you first hear that, it sounds like a cliche description of soul-searching. But he means it very literally. Borden has asked himself that a thousand times; or rather, Alfred has asked Freddie a thousand times. And the only way Alfred could "not know", is if Freddie insists he tied the simple slip knot, and Alfred doesn't believe him. If Freddie said he'd tied the Langford Double, Alfred would know the answer to Angier's question. But he doesn't.

So Alfred thinks Freddie is a liar. Would lie even to Alfred. That's pretty remarkable.

That leads to another idea: at least part of the diary is genuine. Angier reads it and observes Borden's "divided mind": that suggests both men taking turns writing in the diary. I think Borden took an existing diary, and either EXTENDED it with fake entries up to the point where Scarlett "steals" it; or re-copied it over with the Tesla cipher and fake entries toward the end. Creating a diary from scratch would take a lot of work: easier to use existing entries.
(By the way, if part of the diary is genuine, then Borden is exposing his "divided mind" to Angier, betting that Angier won't understand the secret.)

When Borden ties the knot on Juiia the night she drowns, it's Freddie performing. He shares that significant glance with Julua, which tells us that he ties the Langford Double. And she wasn't able to untie it, as Michael Caine had predicted.

Alfred goes to the funeral.

When Angier goes to Borden's magic show. Alfred is performing that night. Angier holds the gun on him: he still doesn't know, doesn't have any better answer for Angier. So Angier shoots him. This is kind of a cruel irony: the one who didn't do it is shot as punishment. But that means Freddie has to bite down on the stick and take the maiming in cold blood (it's Freddie whose fingers are "still bleeding").

Nazgul's answer here about who's who is right on the money, as I see it, though I differ with him in that I think the twins discussed it a lot. They fought about it. We already know they argue: we see the twins fight & yell at each other once, in the scene where they can't figure out how how Angier does "The Real Transported Man". When Alfred tells us he's "asked himself" a thousand times which knot he tied, those discussions wouldn't have been any less heated.

Nazgul also observes that Freddie is less mature than Alfred, and I think that's important. Freddie ties the Langford; Alfred gets shot in consequence. Freddie starts the affair with Scarlett; Alfred loses his wife in consequence.** Freddie is the one who can't leave Angier alone, and goes below stage at the final performance – but this time Freddie suffers the consequence, gets hanged.

So anyway: that's it. The smart one ("Freddie") tied the knot; the nice one ("Alfred") faced the questions. Offscreen they had many an argument about it, going over the events again and again. Freddie always insisted he tied the right knot, the simple slip. Alfred didn't believe him.

**The way I wrote that sentence minimizes Sarah. As if it's more important that Alfred loses someone than it is that Sarah dies. That's not my view, I'm just going for the parallel sentence construction here, for this point about Freddie compared with Alfred.