The Chinese Syllabary
The best explanation for thinking about the Chinese writing system as a syllabary is embedded in the FAQ page of Zhongwen.com. In response to the question "How do you know the pronunciation of a character" Zhongwen.com provides this answer.
Chinese characters do not have an alphabet but they
incorporate a rough syllabary. Whereas alphabets
use symbols to represent each phoneme, syllabaries
use symbols for each syllable. ... When a language has
few syllables a syllabary has clear advantages over
an alphabet. Children have less difficulty dividing
words into syllables than into phonemes. (Many
adult Chinese unfamiliar with alphabet-based writing
systems have a very hard time writing even their own
names in Pinyin since it requires phoneme-by-phoneme
dissection of the syllables. And syllabaries allow for
quick reading because the symbols can be made quite
distinct from each other rather than just being letters
in different combinations arranged in a line.
More on why some people call the Chinese writing system ideographic another day.