Rider
Rider stood waiting for their response. However, instead of addressing the situation with Shirou, Vanguard made a different point.
"Rider, I cannot allow Sakura to be left here exposed to danger. If we were to both go out to look for that impudent animal, who would protect her and her husband from whatever danger lurks in this city? If an attack came to be, she would be defenceless. Besides, it is not prudent", he said.
"I very much doubt Sakura would be glad to lose you, Rider. I do not wish to have another friend taken from me either. Please, be careful and do not act in a way that would compromise you or my master."
Rider pondered his words. Whilst Sakura was unlikely to be attacked in her own house, they couldn't be certain, and leaving her undefended, particularly in this state, was not a good idea. Especially now that Faust's demons were no longer here to protect her. So, one of them should indeed remain to protect Sakura. But, which one?
Vanguard certainly made a convincing case. She remembered how pleased Sakura had been when she had agreed to form the contract, how happy Sakura had been to see her old friend and loyal servant again. If she were to die, Sakura would be devestated. Vanguard, on the other hand, was not someone Sakura was as closely attached to. She could cope with his death far more easily than with hers.
Before Rider could make any comment, though, Rin spoke.
"You know, Sakura's perfectly able to take care of herself", she said, her hand drifting to the wound Rider knew Sakura had inflicted on her back in the cavern where Rin had confronted the darkened form of her sister. "But Shirou on the other hand . . . He's gifted on one set, but you're right Armor-san. Someone should stay here to protect Sakura and Shirou".
Rider chuckled at Rin's nickname for Vanguard. Whilst she didn't quite agree with the girl's logic regarding Sakura's ability to defend herself, nevertheless she was right that someone needed to remain. Rin, though, had not finished speaking yet.
However, Rider, I think your Emiya should come with me and whoever doesn't stay. We might be able to reunite him with his Sakura and three sets of eyes are better than two, especially if they're as good as his", she continued.
"Now the question is, who's going to play baby-sitter. Armor-san, we're going to have to talk to people and most people might clam up if they see someone like you. However if there's a fight you might be more durable than Rider. So, should I get some straws for you two to draw?"
Rider pondered the situation once more. In individual terms, Vanguard was more expendable than she was. Sakura could cope with his loss, whereas she could not cope with Rider's. Rin's logic itself was a mixture of the only-vaguely-relevant and the downright incorrect. Ultimately, what mattered most in making the decision was ensuring that Sakura's already-fragile mental state would not be worsened yet further and, to that end, Rin's logic made little difference.
However, Rin's speech reminded her that she would be there too. And, she seemed to want them to bring Shirou as well. Whilst her own survival was important for Sakura, Rin's was paramount. Further, whatever it was that had killed Faust was surely too powerful for Shirou or Rin to handle. Thus, if Vanguard died, then surely they would quickly follow. And, contrary to Rin's assertions, Vanguard was not significantly more durable than Rider, and he was most certainly slower and much less powerful. Rider knew that she would be far more capable in a fight and, thus, far more likely to win. Further, if the worst did come to pass and the enemy proved to be too strong for them, Rider could out-run almost any pursuer, particularly if she was able to summon Bellerophon.
And, that was without even considering Shirou. Whilst this Sakura likely didn't care about him one bit, her original master certainly did. Rider could never allow her to suffer the pain of losing her beloved husband. She would protect him, even with her own life if she must, just as she would Rin. Vanguard, on the other hand, had no reason to care about Shirou and nor, to an extent, did Rin. Rider could easily see Vanguard leaving him to die if the situation warranted it. So, she simply had to be present, to offer him the protection he needed.
Sighing, Rider turned to address the two of them.
"Vanguard, whilst you are right that Sakura would miss me if I died, I think I still have to go. Whatever it was that killed Faust has to be powerful, I am not sure you could defeat it alone. And, if you were to lose, Rin and Shirou would be defenceless. I am stronger than you, and much faster. Not only am I more likely to win, but if the enemy turns out to be more powerful, I am far more likely to be able to get Rin and Shirou to safety", she said.
Then, suddenly, Rider had a brain-wave.
Wait, this Sakura still has a command spell.
"One other thing. I just remembered that Sakura has a command spell remaining. If she gets into trouble, she can call me back here instantly. Further, she can communicate with me mentally, so she can remain in contact with me in a way that she cannot with you. I should definitely go, since I can return if trouble arises. You may wish to come too, Vanguard. I could not easily beat Faust in a fight, so I would not expect to be able to easily defeat his killer either."