Why Do Nepalese And Indians Think Buddhism Is A Branch Of Hinduism?

This is a very complex issue that requires proper understanding of these two religions (Dharma) as well as their historical evolution in the Indian subcontinent. However, the following points can give us an idea as to how this misunderstanding took hold in the Indian-subcontinent:

Historical

1. Hostility of Vedic Hinduism: Buddhist and Hindu texts are both witness to the hostility of Vedic Hindu followers towards the Buddha and Buddhism, and the proponents of Vedic Hinduism tried their best to repress this new movement that had started to spread like wildfire across ancient India and was beginning to have a serious impact on their religion, especially as the Buddha refuted Vedic philosophies and traditions, such as the system of caste and stages of life (varṇa-aśrama-dharma).
2. Persecution of Buddhism: For the above reason, Buddhism was repeatedly persecuted by Hindu leaders and Kings in ancient India.
3. Spreading misinformation: Apart from persecution and repression, spreading misinformation about the Buddha and Buddhism was another ploy used by adherents of Vedic systems. Inclusion of the Buddha as an incarnation of Viṣṇu (in the 2nd-3rd century), for example, was one such move, which would eventually help to dilute Buddhism and co-opt it and theBuddha into the Vedic Hindu fold.
4. Disappearance of Buddhism: Due to Vedic Hindu persecution and the Islamic invasion that resulted in the destruction of great Buddhist universities such as Nālanda, Vikramaśila, etc., Buddhism slowly started to disappear from the Indian subcontinent from the 11–12th century onwards.

Philosophical

1. Buddha’s Dharma can be difficult to understand. Its philosophy is subtle and profound and occasionally hard to grasp, especially for someone who comes from a strong theistic religion or for those who believe in some kind of permanent core — such as ātman/brahman, etc. Most Vedic Hindu scholars, Panḍits, Bābās, etc. misunderstood, misconstrued and misinterpreted core Buddhist philosophies, especially the Buddhist point of view (dṛṣṭi) on the nature of reality — i.e., dependent origination (pratītya-samutpāda). ) On account of this, a distorted form of Buddhism started to spread among Hindu followers. After Buddhism disappeared in India there was nobody to correct such misinterpretations.
2. Vedic Hinduism believes in inclusion and eclecticism; this is based on certain Vedic injunctions, such as “ekamsat viprā bahudhā vadanti’ (There is only one truth but the wise express them in various ways). Having reconciled with the abundant contradictions and anomalies within their own tradition, Vedic Hindus approached Buddhism with the same attitude, believing it to be just another renegade branch of Vedic Hinduism. This created an obstacle in understanding Buddhism as it is. Instead, Vedic Hindus made several attempts to incorporate Buddhism within their system, especially once the latter disappeared from India. Such acts — including the assimilation of Dharmas that totally contradict their own core philosophy —  are taken positively in Vedic Hinduism.
3. Vedic Hinduism and Buddhism often use the same languages, such as Sanskrit. This has created ample confusion, even though the type of Sanskrit used in Buddhist texts is often substantially different from Vedic or Classical Sanskrit. Hence, Vedic scholars/commentators started to misinterpret Buddhist Sanskrit and introduced wrong ideas and distortions without understanding the Buddhist point of view or its usage of grammar, which is based on its own interpretive systems. They failed to understand that Buddhist Sanskrit is a different category of the Sanskrit language.

Cultural/Sociological/Political

1. Both being religions of the Indian Subcontinent, Vedic Hinduism and Buddhism shared many cultural elements, and Vedic traditions absorbed many Buddhist elements over the course of time. However, once Buddhism disappeared from India, these became increasingly difficult to distinguish and the philosophical differences were concealed by cultural similarities.
2. After the invasion of Islam, there was a necessity in India to find a common ground for all religions, including that of the invaders. This sociological situation gave rise to philosophical ideas such as the equality of all religions, their singular goal, etc. Such social movements started to entrench themselves within popular beliefs; poets and mystics started to write on such themes, and this captured the mind of the masses. As a result, bhakti movements became the prominent spiritual traditions in India/Nepal. This again masked philosophical differences.
3. The Islamic invasion, as well as colonization, weakened Vedic Hinduism; the culture of reading spiritual texts eroded, and gradually Vedic Hindus became ill informed about Indian religions, which continues to this day.
4. After colonization, out of nationalistic fervor, Vedic Hindus started to dream of uniting all the faiths in the Subcontinent, and made claim to a great “bhārat” in order to reclaim their lost glory. Such political and sociological moves further introduced distortions and misinterpretations, denying the distinct philosophical and spiritual tradition of Buddhism. Recently, the Hindutva movement is helping to reinforce this belief — i.e., ‘Buddhism is not a separate spiritual tradition’.
5. Since Dr. Ambedkar employed Buddhism to tackle sociological issues concerning the outcasts and lower castes in India the elitist Brahmins/Political leaders/scholars have found it even more important to include Buddhism within its fold.

These are some of the reasons why today Hindus in Nepal and India do not understand that Buddhism is a separate spiritual tradition, outside the pale of Vedic religion.