Not necessary, because the argument never argues that something should or should not be done. So it doesn’t need to assume anything about the circumstances necessary for when class sizes “should” be reduced.

Not necessary, because if it were not true — if NO qualified teachers would be able to improve overall achievement in their classes if class sizes were reduced — this doesn’t undermine the argument. In fact, it helps support the claim that reducing class sizes would not improve overall student achievement.

What students value has no role in the reasoning of this argument. The argument concerns the effects of making class sizes smaller. We have no reason to think what students value more has any impact on the effects of reducing class sizes.

Not necessary, because it’s too extreme. The author doesn’t need to assume that underqualified teachers would not improve the achievement of “any students in the school.” Even if they improve the achievement of some students, as long as they don’t improve the overall achievement of the school, the author’s reasoning still stands.

Necessary, because if it were not true — if qualified teachers COULD be persuaded to relocate in significant number to the educator’s region to take teaching jobs — then the fact that there’s a shortage of qualified teachers in THIS REGION doesn’t necessarily establish that we’ll need to hire underqualified teachers to reduce class sizes. We might be able to hire qualified teachers who move in from other regions.