Why is Buddhism followed mainly outside of India when it originated there? India is the original land of Buddhism, but it is followed/practiced more outside its country of birth. Are there any reasons for this?
India (the modern country) didn't exist when the Buddha was born.
The Buddha was born near modern-day Northern India or Nepal.
Wikipedia's Decline of Buddhism in the Indian subcontinent says,

[This] refers to a gradual process of dwindling and replacement of Buddhism in India, which ended around the 12th century. According to Lars Fogelin, this was &quot;not a singular event, with a singular cause; it was a centuries-long process.&quot;
The decline of Buddhism has been attributed to various factors, especially the regionalisation of India after the end of the Gupta Empire (320–650 CE), which led to the loss of patronage and donations as Indian dynasties turned to the services of Hindu Brahmins. Another factor were invasions of north India by various groups such as Huns, Turco-mongols and Persians and subsequent destruction of Buddhist institutions such as Nalanda and religious persecutions. Religious competition with Hinduism and later Islam were also important factors.

This History of the Delhi Sultanates says,

Between 1160 and 1187, Muhammad al-Ghuri conquered the Ghaznavid Empire; he continued to expand his territory, and in 1192 he razed the Buddhist temple complex at Nalanda to the ground, in effect terminating the history of Buddhism in India.

It references a student's paper on the The History of Persecution of the Buddhist Faith, which includes,

Among the destroyed temples, 2/3 were Buddhists, and this was critical to Buddhism's ability to remain as a formal religion because they had already lost all but a few institutions in Nalanda, Odantapuri, and Vikramasila, over the previous centuries. (20)
The Nalanda University, a great Buddhist center of learning, was raided by Turkic Muslim invaders under Bakhtiyar Khalji, a general of the Turkish commander Qutb-ud-din Aybak, in 1193. He committed documented executions, harassed and tortured erudite monks, killing 15,000 scholars and 200 faculty of the University. (21) The campus and invaluable works of art including the images of the Buddha were destroyed and the enormous manuscript library of the University was burned down. He also destroyed the monastries in Vikramshila, which were in modern Bihar, as well as many monastries in Odantapuri in 1197. As he persecuted Buddhism, he supported Muslim missionaries and made the biggest number of converts to Islam under his reign. (22) By the end of the 12th century, many Buddhist monks retreated to Nepal, Sikkim, Tibet and Southern India. (23)
Persecution of Buddhism was accelerated in this period by Brahmin revivalists who kicked the Buddhist monks out of Buddhist monasteries and temples in order to transform the places into Hindu institutions; they were seeking protection from Muslim invasions by facilitating the installation of Brahmin gods. (24) No less than 1000 Buddhist temples were appropriated by Hindus, etc.

The (numbers) in the quote above are references to various history books etc.
There's a Wikipedia article (whose neutrality is currently disputed) titled Persecution of Buddhists which includes,

In 1200 Muhammad Khilji, one of Qutb-ud-Din's generals destroyed monasteries fortified by the Sena armies, such as the one at Vikramshila. Many monuments of ancient Indian civilization were destroyed by the invading armies, including Buddhist sanctuaries[45] near Benares. Buddhist monks who escaped the massacre fled to Nepal, Tibet and South India.[46]

... and continues in a similar way.
Perhaps these are the reasons: i.e. they're historical reasons.
It might seem as if it would be interesting to try to answer this question by discussing 'motive' (e.g. &quot;why would people prefer to be Hindu than to be Buddhist&quot;), comparative religious views (e.g. about 'just war'; and about how well the religion is integrated into the broader society at large), and comparative values (which religion is more useful, more attractive, more true) but I expect that would be subjective opinion, off-topic and unhelpful.

I'd also mention this answer to the question, Were Buddhists murdered en masse during the first Muslim conquest of India?
It references a thesis which says that Buddhism declined (not especially violently) during the 200 years or so following the first Muslim invasion -- i.e. in the 8th century AD -- mostly because urban merchants (who previously supported Buddhist monks) converted to Islam for various reasons; whereas the more-Hindu farmers were relatively unaffected.