Why paganism in Europe died, where polytheism in Asia survived?

It's because Christianity incorporated a lot of pagan rituals into Christianity and some pagan gods became catholic saints.

The crusades targeted all religions that weren't nicene christian and they were especially cruel if you were christian but not nicene.

Lookup the history behind the Dominican order if you want more gory details

Roman empire prosecuted Pagans in later eras in same way they prosecuted Christians in earlier eras. All countries in the Roman empire were dominantly Christian.

Asians were not part of Roman empire neither did Arab for that matter so they maintained paganism until eventually Islam eliminated it from Arab region and so only Asia survived

The fucking inquisiton

Besides the other reasons mentioned here, i think there is a strong factor in the social and intellectual sphere. Christianity was a cohesive standardized institution with a written holy book (or set of texts, before the council where they canonized which books would go to the bible), and later became a part of enforced state policy. That mixture of standardization and officialdom allowed it to essentially accumulate 'capital' to such a degree it could (after absorbing lots of ideas and practices) overwhelm the local polytheistic societies and religions.

Local polytheistic religions were extremely varied, and each village tribe or city had its own gods, beliefs, etc. The mess of beliefs meant that the religions spread organically, not in an institution with quasi industrial ways (standardized beliefs, practices, texts, even rows of clergy trained in the same ways on churches and monasteries). They could be challenged and be overwhelmed by the bigger faith, in intellectual ways (evangelization) or by demographic superiority. Or just by immigration to other regions (which many people did, like the barbarians in late Rome or Imperial legions and soldiers since always), where multiple contradictory faiths coexisted, until a cohesive unified alternative popularized.

All that is inverted in India. Hinduism was (is) varied, but way less than paganism from ireland to iran, and it is a formalized institution with written holy texts supported by the state (or by castes, specially the Brahmins), very constant and stable over many generations. That inertia even allowed it to not become muslim majority (except in a few regions).

Other countries in Asia actually have Buddhism as the main religion or state religion (or main historical religion). Even if buddhism absorbs lots of pagan deities, ideas and praxis, the core institution is solid and formalized, and dominant. Japanese Shinto is very different from pre buddhist times. China had buddhism, and confucianism and taoism as also very standardized formalized state institutions (aka not a different religion per village). So asian polytheism is very reduced compared to european one.

I think a major factor was the Hellenistic age (the spread of Greek culture from the Mediterranean to Central Asia after Alexander the Great) and the “interpretatio graeca”—the practice of the Greeks (and later Romans) of merging their own polytheism with the various other forms of polytheism they encountered in the Hellenistic world. The result was that everyone from the Celts and Germans in western Europe to the Egyptians and Iranian polytheists in the Near East (but not the non-polytheistic Jews or Zoroastrians) could be assimilated into Greco-Roman culture without formally giving up their religions. But a side effect was that all religious institutions were assimilated into the state, so that when the state switched to monotheism there were no independent religious institutions to oppose it.

One factor is that paganism is tolerant of adding additional gods, practices, or beliefs to your mix. From a pagan standpoint, adding in Christianity wasn't a big deal, but Christianity was not similarly tolerant, they weren't cool with you keeping your pagan gods. Plus their belief system had the threat of eternal damnation and the promise of heaven to motivate you.

Christianity

Within the Roman Empire, Christianity ended up succeeding as the apocalypse cult within the empire, with Rome eventually foresaking the old gods for Jesus.

As Roman retreated, Rome's church survived and became a unifying force in Europe. While there were crusades, there were also cases of willing conversion in order for border nations to gain access to the European market and diplomacy.

tldr: Pagan Mongol tribes

I theorize: Nomadic mongol tribes (horsemen who used bow and arrow to hunt 🏇🏹) converted quite quickly to the religion of the people they conquered. But the Mongols where mostly pagan shamanistic tribes in the beginning (they believed in the Sky god Tengri) and transferred some of their culture into ruling elites of their subject countries and killed many monotheistic farmers people greatly altering east asian and central asian demographics at a scale of 40.000.000 people 💀. Also the Mongol conquests acted as a buffer that kept Islam or Orthodox Christianity spreading beyond central asia into east asia for 500 years:

• Mongol tribes captured Moscow and beyond, preventing orthodox Christianity to expand to China faster
• Mongol empire captured the Chinese capital Beijing. Maybe their shamanistic believes influenced locals.
• Timurid (emperor Timur was grandson of Mongol Ghengis Khan) empire only expanded west not to China by their luck. They defeated mostly muslim empires like Persians and Ottomans. This prevented larger muslim expansion into east Asia. Even Europeans viewed the muslim timurids as a great threat, but also as a ally against Persian and Ottoman empires.
• The siege of Baghdad in the year 1258 by the Mongol empire with Chinese siege-craft destroyed the Muslim "golden age" destroying a chance of their expansion to east asia

Additional theory: Shamanistic Mongol tribe invasions might have deeply altered the subconscious of the religious people they annexed in central Asia/Eastern russia and Persia, what is known that they replaced the ruling elites and subtly influenced hierarchy to make taxation easier.