1. Chinese Characters just looks better than an alphabet with tons of diacritics. How many people tattoo Pinyin to look cool?
2. Knowledge of Chinese Characters is seen as a tool that is worth the effort - it gives a different level of understanding of the meaning and words of the language, something that is arguably not immediately available to speakers of English. Who can forget that “tomorrow” is made up of “sun” and “moon” rising and setting, or that “rest” is a “person” leaning on a “tree”?
3. Medical and scientific terminology is far easier to write and understand in Chinese than spell in English. The Chinese word also gives a better clue as to what a given term means, e.g., “肝硬化” literally translates to "liver hardening", ”眼科” literally means “study of the eye”, “儿科” literally means “study of children”, which can be understood even by a low-level, non-native speaker; without more context.
4. The gap between colloquial speech and formal writing can be quite large. For Chinese to be written in Pinyin, Chinese writers would just have to avoid overly ambiguous vocabulary terms and devise some new standard replacements if it became necessary. In addition, writers have to avoid writing in a terse and poetic style influenced by Classical Chinese and more in a informal speaking style. This kind of vocabulary and grammer replacement would have massive linguistic and cultural impacts, similiar to removing all the latin and greek vocabulary in English. It would almost make current formal Chinese writing unintelligible.
5. Chinese Characters allows the Chinese people to access their history and culture directly. Like most technology, backwards compatibility and not ease of learning is a good point for not switching to Pinyin. Switching to Pinyin would cut the Chinese people from thousands of year of culture and history. Every Chinese people is at least familiar with a few lines in ancient Chinese books like Art of War, Analects, Dao De Jing and Han/Tang/Song poetry in the written language. Can you think of a comparable piece of Latin or Greek writing that the average Westerner knows by heart? How many people can recite Virgil and Homer? Bonus if they can do it in the original Latin or Greek. Greek and Latin in the West have been the bastion of the Western civilization, and in this age, all but forgotten.
6. Chinese characters promotes national unity and cohesiveness. The stature of Han Chinese as the largest national grouping in the world can be explained partially by the writing system. All literate Chinese, even if they speak mutually unintelligible “dialects”, can read the same books and feel that Chinese Characters is their own language. If they had a phonetic writing system, they might have broken up into separate national groups, as did the Italians, French, Spanish, Portuguese and Romanian.
7. Chinese characters are part of Chinese identity. From a western perspective it's difficult to truly understand the degree to which Chinese characters are interwoven into Chinese cultural identity. In the West, calligraphy is seen as a niche interest, while in China you have people studying and imitating the ancient calligraphy masters, students taking calligraphy courses, elderly writing characters in parks, families hanging proverbs outside their doors, decorating homes with calligraphic art etc. If Chinese characters were abandoned, Chinese calligraphy would not be the same, all riddles/ jokes/ puns/ poetry would become meaningless, Chinese names would become gibberish. Chinese characters are an extremely emotional issue and are something more than just writing. That is why even the idea of simplifying Characters outraged so many people.