Because he's not the one who tied 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.