ガン, Cancer (Japanese article)
トヨタ, Toyota, car company
バーガー, Burger, Every Burger sweets package
I can understand why the medical community in Japan would choose to use katakana so as to better proximate conditions that perhaps first been named in English, and therein better proximate an international standard or language with regard to medicine. That being the case, I might think cancer to be something more like カンサー, although ガン pretty closely approximates the first syllable. Maybe the word has more punch when it's monosyllabic, it certainly feels to have more gravity to me as such.
トヨタ I understand a little better. It would make sense that a company with international aspirations would want to have their name written in katakana, not only for the reasons of standardization mentioned above but also because katakana is aesthetically simpler than hiragana or kanji and could therefore be easier to copy and easier on the eyes of Westerners. I also think having it written in a language for foreign words gives it an air of internationality the brand probably sought when it made the decision.
バーガー is an obvious one, it sounds like 'burger' in english and is taken from english (well originally german) and as such is written in katakana.
I think the book's explanations of katakana were all good, although the last for me was by the far best. I think they probably explain katakana the way they do to ease the beginning Japanese students of the notoriously complicated 'three writing systems' in making the main focus of their summary "don't worry, once you can read it you'll understand what it's saying!"
