Asian countries have an emphasis on building public transit, and having large effective public transit systems due to several factors (as someone who's from there):
- Population Density: The megacities of Asia just make sense to have strong robust networks based on the population and geography of the areas. The RoI is much stronger there.
- Technological Leapfrogging: This point has been made already.
- Traffic Bottlenecks: If you've ever been stuck in a traffic jam in Manila or Jakarta, this is self explanatory lol. The losses from traffic bottlenecks are in the billions, requiring mass transit solutions
- Ideology: For the case of China and other self-proclaimed Marxist-Leninist states, they've inherited the Soviet legacy of public transportation as "palaces for the people", which makes the focus on this reasonable.
- Cost: Cost of labour is less in these regions.
- Prestige: Strong metro systems are seen as prestigious achievements, especially for rapidly industrializing nations. India did this recently, while also neglecting other facets of public transportation.
- Sino-Japanese rivalry: Both countries are throwing money at infrastructure projects, especially in SE Asia as a way to curry influence.
- Priority: These countries' prioritize metro and public transport for funding and political capital. Simple as.
That's not to say it's perfect. Ho Chi Minh City's metro took 13 years of construction due to delays and issues, kinda like Eglinton Crosstown.