This is just avoiding the issues. "B is younger in A time"? The paradox is explicitly stated in a way everybody can understand as to avoid using additional parameters that make comparisions impossible [of course, only because it is possible to state problems that way doesn't alway mean that you can
answer them as such -- but in this case, it should be possible].
The question is: Assuming both twins die after they lived the same proper time, who is closer to death when they meet again [in other words: Assume both do exactly the same things afterwards, and die a natural cause (=old age), who dies first]? A physically better way to say this is: What twin had more
proper time pass (which equals age)?
Thats a clear question, and it has a clear answer. It is: Twin A stayed in a inertial frame the whole time. Things are easy to calculate in his system, and we find that Twin B will be younger than Twin A (since more proper time passed). Twin B is not staying in an inertial frame the whole time - things are difficult to calculate in his frame. But there really is no need to, since we already got our answer earlier.
The actual, easy, straight answer to all of this is: The twins age differently since their pathes are different in spacetime, and thus have different lengths.
Saying "A time" or "B time" isn't
wrong, but it isn't helpful, either. It's good to establish that there is no such thing as absolute time, but we cannot really say anything about A's age in B-time. In other words, your statement:
A is younger than B according to the B time
is correct if Twin B would be moving in one direction at the same velocity forever. But the essence of the twin-paradox is that he's
not, he went back, accelerated and thus "changed inertial frames".
EDIT: I read your post again, and now I'm not sure what you're arguing, to be honest. It seems you're stating that there is a paradox* sometimes, yet that there isn't at others.
* - for the sake of the argument, I've called it "paradox", even though we've already established that it isn't one. But even that seems weird, because, as I've stated, the "twin paradox" actually refers to
two things. Which are we arguing about? Who can even tell...
