Final answer:
The example provided is a slippery slope fallacy, where a small step is predicted to lead to a significant negative outcome without proper evidence.
Step-by-step explanation:
The statement 'If we allow the government to require healthy meals in school cafeterias, then it's only a matter of time before the government tells us everything we can and cannot eat' is an example of a slippery slope fallacy. This type of fallacy asserts that a relatively small first step will lead to a chain of related events culminating in some significant negative effect, without providing any substantive evidence that this dire outcome is likely to occur. The slippery slope is a subcategory of fallacies of weak induction, where the evidence provided is relevant but insufficient to justify the conclusion.
A clear example of a slippery slope fallacy can be seen in advertising or political scenarios. For instance, a commercial might suggest that failing to purchase a particular type of insurance could eventually lead to financial ruin, even though this is not a guaranteed outcome. This fallacy preys upon the audience's fear of negative consequences to persuade them, instead of presenting logical reasons why the projected outcome is highly probable after the initial step is taken.