Exposure to America's space program could provide China with access to dual-use technology that they don't currently possess. Look into the Loral Space Systems controversy from 1996. From wikipedia:
Loral was accused of transferring technology to China in 1996. The incident arose as a result of an investigation into the launch failure of Intelsat 708, a Space Systems/Loral–built satellite. In a 2002 agreement with the State Department and Department of Justice the company agreed to pay $20 million in fines to settle the matter and to improve its compliance procedures. In the agreement Loral officials neither admitted nor denied the government's charges, but Loral executives acknowledged "the nature and seriousness of the offenses alleged by the department in the draft charging letter, including the risk of harm to the security and foreign policy interests of the United States", and stated that they wished to make amends through the payment of restitution. Schwartz subsequently released a statement accepting "full responsibility for the matter" and portrayed the incident as an error by a single Loral employee.
Far from being a tour-de-force of Chinese espionage, this rocket technology leak apparently happened because a Loral employee accidentally sent a single internal Loral post-mortem document by fax to their Chinese partners. Its almost impossible to keep secrets when there's close business cooperation like this; accidents happen.
