It's not infrequent that an applicant tells me that a letter of recommendation (LOR) writer has asked the candidate to draft his/her own letter because the writer is "too busy." I notice that medical school and residency applicants are a bit sheepish as they tell me about this arrangement. Have no fear: You are not doing anything unethical. (Here is an old piece by the New York Times ethicist Ariel Kaminer regarding this exact topic.)
If a faculty member asks you to write your own letter, not only should you do it, but you should do it with zeal. Make sure you showcase the accomplishments that distinguish you from other candidates and highlight traits that are important for your future career path. Use honest - but bold - adjectives to describe your best qualities.
Remember that the letter writer has final say, so even a busy faculty member might modify the letter. Keeping this fact in mind might alleviate your (unnecessary) guilt and should encourage you to write the strongest letter you can. (It's harder to go from outstanding to mediocre than from outstanding to excellent.)
