The argument presented is that changing the set-lunch menu available to students in schools, and offering healthier options, will help inculcate healthy eating habits and reduce the incidence of obesity.
Option A talks about the pricing of the new, healthier eating options. While pricing may be an important consideration, it is not necessary for the argument to hold. So, option A is not required for the argument to hold.
Option B talks about the support of parents for the proposed changes. While parental support may be desirable, it is not necessary for the argument to hold. So, option B is not required for the argument to hold.
Option C talks about the impact of the proposed changes on the number of people considered obese in the country. This statement is not necessary for the argument to hold as the argument is concerned only with the impact on school children, not the entire population. So, option C is not required for the argument to hold.
Option D suggests that a significant number of students do not eat healthy meals at home. While this may be an important consideration, it is not necessary for the argument to hold. So, option D is not required for the argument to hold.
Option E is required for the argument to hold, as it suggests that more than 50% of the students rely on the school's set-lunch menu, and hence, the availability of healthy options at school will be critical in ensuring they have healthy meals.
Therefore, option E is required for the argument to hold, while the other options are not necessary.