I'm not certain that Taylor's precog can be blamed entirely for not attempting to argue her position with Danny. It appears he wasn't going to even contemplate negotiating his position with Taylor, or accept the possibility of other alternatives, merely confronting her with his mind already made up. If any of the potential outcomes had been along the lines of "I'll have to think about that", as opposed to her arguments being dismissed, or worse driving him more firmly into his pre-established position, I can't see that not being seen as a win, if only a small one.
I suspect that Taylor may have been willing to accept an affiliation with the Wards, where she can discover from the only sources she'd be willing to trust, the Wards themselves, that, much to her astonishment and surprise, the PRT, unlike her recent experience, is neither willfully blind, nor out to screw her over because the pretty people cry crocodile tears. At that point a full membership in the Wards becomes just that much more likely. Probably the entire point for the existence of what Piggot offered to Taylor.
That seems to be a pretty good reason to me, and I still remain baffled that "unspecified arguments which break Danny as a person" came before "you think signing on with the group that wants to recruit the girl who made my life hell for years and tried to murder me at the school you sent me back to will make me safer?"
If it was mentioned to Danny that Sophia wasn't
asked to join the Wards, as opposed to being
forced to join the Wards as a way to keep her under control, I doubt that that argument would hold much sway. Of course, if he doesn't mention the reason the argument carries no weight is that Sophia's recruitment was a punishment, and I'm fairly certain it wasn't spun that way by Miss Militia when Taylor found out, it's going to be filed under "Arguments that are important to me that my dad's just going to ignore, because my opinion obviously doesn't matter, as he's already made up his mind".
Hmm... I wonder if Browbeat is going to be called onto the mat when Taylor finds out that Madison == Browbeat? Sophia's gone, Emma's apologised, though I seriously doubt that she's anywhere near forgiven... but Madison was the one who managed to get the system to screw Taylor over (or at least supplied the crocodile tears for doing so). I can't help but think of a look of glee on Taylor's face as Madison becomes a valid target for some payback, err... sparring. It would be extra vicious if she ever finds out why the Trio was getting away with things was because of Madison. I imagine Madison's reaction would be the standard sociopath (I think) one... "I just kicked the dog every day when I came home... why would it suddenly decide to bite me?"