Two critical facts
1. The islands and seas within China's nine-dashed-lines map were discovered and claimed by China 2,000 years ago. China was the first discoverer and claimant of the South China Seas.
You can read about China's historical claims to the South China Seas over the last 2,000 years in the Chinese imperial dynastic records. There are also plenty of Chinese shipwrecks, buried bones, and buried artifacts (including wells) within the nine-dashed-lines map. China was there first and it belongs to them.
2. Among the South China Sea claimants, only one of the countries has a real navy (see videos below).
Combining points #1 (e.g. only China is the legitimate owner) and #2 (e.g. only China has the naval power to back its claims), it is clear that only China can claim sovereignty over the South China Seas.
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Published on Feb 13, 2013
A People's Liberation Army Navy fleet is on their way to Qingdao Port in northeast China after they finished intensive training missions in the West Pacific. During the training, the fleet held drills about attacks and defense, air defense and anti-submarine and over-the-horizon attack. Meanwhile, the training tested tactics, technical performances and computerized remote capacity of supplies."
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Published on Nov 23, 2012
The Chinese People's Liberation Army Navy recently carried out live ammunition drills in the South China Sea and East China Sea. Vessel-airplane confrontation, vessel-submarine confrontation, air-defense and light weapon shootings were completed in the drills."
[Note: Don't bring up the United States. The U.S. does not recognize UNCLOS, is not a claimant to the South China Sea territory, and Chinese megaton EMP warheads can easily neutralize any American surface fleet.]