The author doesn’t have to assume over half (”most”) of new jobs created will be in fields that “pay well.” Even if that’s not true, we still know that many day-care care workers will quit to take “better-paying jobs” in other fields.

Necessary, because if it were not true — if the number of new day-care workers WILL be significantly greater than the number of day-care workers who move to other fields — then the author has not established that the increased demand for day-care would have to exceed the increased supply for it.

Not necessary, because even if the number of workers employed by day-care centers is NOT likely to decrease, we still know there will be increased demand for day-care. Although the author must assume that the disparity in demand and supply for daycare will increase if the economy grows stronger, this doesn’t require day-care supply to go down. Even if it stays the same, an increased demand for day-care would still increase the disparity between demand and supply.

Not necessary, because although the author does believe that day-care centers quitting to take better-paying jobs in other fields is something that would worsen a shortage of day care, the author doesn’t have to believe it’s necessary. If there are other things that would also widen the disparity between the demand for day-care and the supply of it, that doesn’t undermine the author’s position.

Not necessary, because the argument doesn’t rely on claims concerning the “cost” of day care. The author doesn’t have to have any opinion about the effect of a change in cost of day care.