Because the statistics are produced by local apparatchiks, and the local apparatchiks all want their jurisdiction to look like it's breaking records so they can get promoted and become something bigger than a local apparatchik. And the central government wants to look successful too, so nobody there has any interest in pushing back. High numbers mean everybody in the system wins, while low numbers profit nobody, so the numbers come out high.

Chinese GDP is suspiciously stable at exactly the same value for long periods of time, and doesn't seem to correlate with other statistics that usually do correlate, like electricity usage.

IIRC it's not even a secret that China's GDP stats are useless. It's a problem the government has officially admitted to. As a sibling comment notes, the issue is that they aggregate stats from regional governors who are incentivised to tell the party what it wants to hear.

A country might want to inflate their reported GDP to make the country look more attractive to foreign investment.