I've argued elsewhere that it depends on cultural importance of blood lines. In particular, whether surnames arose as a mark of lineage, or for ease of identification. I believe that applies here as well:
Cultures with strong views of family tend to adopt a collective representative name. In those without, surnames tend to come about for identifying otherwise similarly named individuals. It would have been convenient, and would indeed make sense, to identify a wife by her husband's name ("Agnes who married John the smith; not Agnes who married John the carpenter"). Then as surnames became more established, dropping maiden names turned into an ingrained traditional custom.
Historically, Chinese surnames had two components: a clan name,
姓, and a household name,
氏. The former was shared by the whole clan, and normally remained constant for generations. In contrast,
氏 denoted different branches of the extended family. It frequently changed as families adopted new ones based on placenames, professions, job titles, etc - rather like how English surnames developed. This system persisted till the late Warring States period.
If we look at the word for clan names,
姓, it is obviously a composite of the radicals
女, meaning woman, and
生, meaning birth. Thus, from its earliest times Chinese surnames had been intrinsically linked to (matrilineal) kinship. Of course, bloodlines do not usually change with marriage. Likewise, it wouldn't make much sense for a woman to change her surname to her husband's.
Furthermore, Ancient China was most likely originally a matrilineal society. In fact, the Eight Great Clans of Antiquity,
妊 - all contains the female radical
女. While not an absolute rule, most surnames from the period share this feature. This is commonly believed to be the lingering influences of a matrilineal prehistoric society.
I'm not saying the difference between China and English countries is purely due to patrilineality vs matrilineality, but these factors help explain the different paths of development the two societies took. Moreover, once a tradition became established, it can be very difficult to break.
Sidenote on the Eight Great Clans (exact composition differs depending on source):
姬 - the Royal Dynasty, and rulers of Jin, Wei, Wey, Zheng, Han, Yan, Lu, etc.
姜 - the ruling houses of Qi, Shen, Lü, etc. Claims descent from the Yan Emperor.
嬴 - the ruling houses of Qin, Zhao, Huang, Liang, Xu, etc. Claims descent from Yi.
姒 - the ruling houses of Yue, , Qi, etc. Claims descent from the Great Yu.
媯 - the ruling houses of Qi (post-coup), Chen, etc. Claims descent from Emperor Shun.
姚 - claims descent from Emperor Shun.
妘 - claims descent from Zhuanxu.
妊 - claims descent from Fu-hsi.