Final answer:
The speaker is guilty of using the fallacy of False Dilemma in their reasoning.
Step-by-step explanation:
The speaker in this scenario is guilty of using the fallacy of False Dilemma in their reasoning. False Dilemma occurs when only two options are presented as though they are the only possibilities, when in reality, there are more options available. In this case, the speaker claims that the only choice is to adopt a vegetarian diet or die of cancer, ignoring the fact that there are other factors that can contribute to cancer and other dietary choices that could be healthy.