Why do some people say the Mongol Empire was responsible for Europe's rise?
1. It presumes that China or Persia or Central Asia would colonize Europe or at minimum remain a great power if Genghis Khan was never born which is impossible to prove.
2. It ignores the fact that the Mongols did invade Europe. They wrecked Eastern Europe and even Central Europe yet those areas eventually recovered.
3. It doesn't explain why India and North Africa got colonized by Europeans when the Mongol Empire never conquered them.
If anything, the discovery of North and South America have far more to do with European growth than the Mongolians ever did.