If you think about it, in reality, Yuri not dying at this point does benefit Operation Strix, although not in the way Twilight realizes.
The mental gymnastics needed to explain why him sparing Yuri was "for the mission" are insane. When Yor asked him to marry her, it was for her camouflage. He KNOWS this, she made it clear. What she mentioned was for "her brother's peace of mind" was showing him that she has someone in her life who cares for her, so Yuri could stop worrying too much and being, frankly, a little overbearing.
On the first phone call we see of them, Yuri asks if she's found a guy, she feels mild annoyance by it but hides it, and then he suggests he could set her up with someone. Yor, being very NOT in the mood for a relationship, let alone being forced into one, tells him she has a boyfriend to throw Yuri off.
But then Yuri proves he has means to find out about said "boyfriend", and thus begins Yor's need for a cover. That's why she asks Loid to pretend to be her boyfriend. It's just that she has already been given the hint that single women her age are considered suspicious, so after he accidentally introduces himself as her husband, she goes like "Welp might as well use that and ask him to marry me so I can have a cover for my assassin job." It's just that Twilight doesn't learn about the "assassin" part.
When Yuri is about to visit, Loid suggests they tell Yuri the truth about why they married, thinking he'll understand. Yor says that no, Yuri HAS to believe that she has found a guy who loves and cares for her.
And so they put on an act. And while Yuri is for the most part convinced about how much they "love" each other, he ends up not approving of Loid one bit.
And Twilight knows that! Yor knows that! Twilight KNOWS that Yor knows that Yuri doesn't approve of Loid. He KNOWS that this marriage hasn't given Yuri the "peace of mind" that Yor aimed for, yet Yor is staying! He saw it that very morning that Yuri still insists on them getting divorced, and that despite Yor having expressed "gripes", she asserted herself and basically told Yuri to stfu.
So, from that point of view, it's absolute NUTS of him to say "If Yor loses her brother then she'll have no reason to stay married to me because our marriage was supposed to give him peace of mind" LIKE BRO!! It already doesn't do that!! And Yuri couldn't have been making it more obvious all this time.
But Twilight needs an official explanation that doesn't include admitting that he did it for Yor's sake and to protect her feelings, because by doing so he'd have to admit he's been emotionally compromised. And a spy like him would have to leave immediately after realizing that. No second thoughts, no back-up plans. Just outright leave.
On the other hand, he is too biased by now to realize how the alternative would actually be the ideal "for the mission". Say he killed Yuri. Yor would be devastated and would need support.
And "Loid Forger" would be there to pick up the pieces.
Maybe not as a romantic partner, but he could definitely take advantage of her bad emotional state to make himself more appealing and essentially "trap" her in the marriage and thus keep Operation Strix afloat.
Which is something he is perfectly capable of doing, by the way. He only spared Yuri because he cared for Yor and knew that his death would devastate her. If it was any other secret police officer, literally any other, he would have killed him without hesitation or a second thought.
So overall, at this point he's just scrambling for excuses, which he should KNOW don't make sense and are just a lifeline he grasps onto because he doesn't want to be let go free in his ocean of "I love my wife and daughter and dog".
But the funny thing is that, unbeknownst to him… in a way, sparing Yuri DOES benefit the mission. How, you ask?
Yor wanted the marriage as a cover for her assassin work. She picked up assassin work to support Yuri's education and protect his carefree life.
If Yuri were to die, she would lose big part of her motivation for staying an assassin. At this point, Loid and Anya especially have also become part of that motivation, but Yuri was the original reason.
So there is a high chance that if Yuri died, Yor would decide to stop working as an assassin.
No Yuri, no assassin job. No assassin job, no need for cover. No need for cover, no use in staying married with Loid.
In fact, it's very likely that she would turn blind for revenge... and being who she is, it's not impossible that she would be able to track Twilight down for killing her brother.
Of course, that's a strict, cold view of the facts. I don't really think that she would leave the Forgers, unless she got too depressed and felt she was a burden to them because of that or had other flight responses to her grief, but she would very likely end up killing Twilight as revenge.
But yes, in a very ironic way, and a very emotionally detached analysis of the facts… Twilight not killing Yuri was actually to the mission's benefit. Even if Twilight doesn't know enough to make that analysis.
It's like a "wrong method but correct result" kinda way, you know?
