YANGZHOU, China—Fan Yue looked into the future and didn’t like what she saw.

As a high-school student in this eastern Chinese city of 4.6 million, she dreamed of going to college and studying education. But most Chinese universities are uninspiring, she said. She heard cheating was pervasive and that many people skip class. Students are required to study “Mao Zedong thought.”

Just getting in takes years of study for the gaokao entrance exam, which is like the SAT on steroids. Students must memorize poetry tracing back to the 7th century. Few of the millions who take it get into China’s top universities, with competition in Ms. Fan’s home province of Jiangsu particularly fierce.

Going through such a process “where I don’t learn anything” would be soul-crushing, said Ms. Fan, 20 years old. “There’s no meaning there.”

There was another option: America. She had heard it was dangerous and wondered if she’d need to carry a knife. Her parents were against it.