How did Jainism/Buddhism challenge Brahmans?

Answer 1

By questioning the religious basis of the caste system. If everyone can achieve Enlightenment in the 'new' religious branches, why should they want to stay mainstream and untouchable for generations?

Answer 2

Challenge To Brahmin Supremacy and Casteism
In the Vedas
Sometimes the Vedas criticize the hymn-chanters. For example, the Rig Veda says:

You cannot find Him who created these creatures: another thing has arisen between you. Those who recite the hymns are glutted with the pleasures of life (high life of luxury they have bought with their undeserved fees); they wander about wrapped up in the mist and stammering nonsense. — Rig Veda 10.82. Translation by Wendy O'Flaherty.
[edit]The concept of Brahmin in Buddhist tradition
Siddhārtha Gautama, the founder of Buddhism lived around 6th century BC. Had it only been for the philosophical tenets of Buddha, they need scarcely have caused, and probably did not cause, any great uneasiness to the orthodox theologians. He did, indeed, go one step beyond Kapila, by altogether denying the existence of the soul as a substance, and admitting only certain intellectual faculties as attributes of the body, perishable with it.

Yet the conception which Buddha substituted for the transmigratory soul, viz. that of karma (work), as the sum total of the individuals good and bad actions, being the determinative element of the form of his future existence, might have been treated like any other speculative theory, but for the practical conclusions he drew from it. He altogether denied the revealed character of the Veda and the efficacy of the Brahminical ceremonies deduced from it, and rejected the claims of the sacerdotal class determined by birth to be the repositories and divinely appointed preservers of sacred knowledge.

Chapter 26 (Verse No. 383-423) of Dhammapada which is one of the most sacred Buddhist text explains how one becomes a Brahmin by his deeds and not by birth. Buddha preached with regard to the final goal, the nirvana, or extinction of karma at the time of death thereby denying transmigration og soul after death. He preched to practice ahimsa in this life to avoid misery which is appealing to the some section of the people. It would be out of place here to dwell on the rapid progress and internal development of the new doctrine. Suffice it to say that, owing no doubt greatly to the sympathising patronage of ruling princes, Buddhism appears to have been the state religion in most parts of India during the early centuries of our era. To what extent it became the actual creed of the body of the people it will probably be impossible ever to ascertain. One of the chief effects it produced on the worship of the old gods was the rapid decline of the authority of the orthodox Brahmanical ritual, and a considerable development of sectarianism Template:Citation needed.

Hope this helps ~

Answer 3

There were two distinct groups of religious thinkers during Buddha's time: one group advocating the belief that salvation had to be attained through Karma marga or Yajan marga, i. e. through the path of sacrifice; and the other holding that salvation is possible only through the path of wisdom or Jnana-marga.

Besides these two religious paths, both put forward by the Brahmins, there was the path to salvation through ascetic practices put forward mainly by such groups as Ajivakas, Paribbajakas, and Niganthas. The latter group belonged mainly to the Sramana tradition which was opposed to the Brahmana tradition. Even the Buddha belongs to this Sramana tradition.

The Buddha who had mastered all the religious traditions of the time not only rejected the prevalent views on salvation, but presented a novel philosophy of emancipation. He discarded such views as divine creation, belief in a permanent self, determinism and annihilationism, and presented his teaching basing it on the fundamental doctrine of paticcasamuppada or dependent co-origination.