Answer:
fallacy of false dilemma
Step-by-step explanation:
The fallacy of false dilemma is a form of fallacy in which it involves the either-or options usually choosing between two options without specifying the availability of other options, even though other options are available.
Hence, in this case, when the letter read in part that "...either loves me or you don't..." This shows the Fallacy of False Dilemma in the letter.