Before I answer this question!, I would like to point out the following:

1. Many supporters of the Manusmriti, commonly known as the Manuvadis, are
supposedly “answering” this question. THEY ARE NOT. They are basically just
leaving comments (not answering). They surprisingly received many upvotes

2. On reading their answers, it is fascinating to note that NO MANUVADI HAS
ACTUALLY ANSWERED THIS QUESTION. (The WHY, the REASONING behind
the burning ). Instead, they have either praised the Manusmriti or have condemned
those who burn it. In their excitement (could be on purpose too), they forget that the
questioner simply wants to know the WHY to an event that occurred on 25th
December 1927.

It’s great to include extra information to support your answers, PROVIDED the question is
actually answered . It does not compute that someone volunteers to answer the question
by AVOIDING to answer the ACTUAL question asked !!

Here’s my answer:

DR AMBEDKAR DID NOT BURN THE MANUSMRITI. IT WAS BURNT BY THE
HANDS OF A BRAHMIN NAMED GANGADHAR NEELKANTH
SAHASRABUDDHE and Dr Ambedkar, along with people of various castes including
the Brahmins were present at the event

Why did Dr. Ambedkar welcome the burning of the Manusmriti Dr. Ambedkar based his philosophy on the belief that the purpose/aim of human existence should be the cultivation of mind. No person should attempt to prevent another person exercising this right.
i.e, in society there must be equality, liberty, fraternity and justice to allow all to fulfill this
purpose.
Dr. Ambedkar saw that the laws in the Manusmriti were counter to establishing equality, liberty,
fraternity and proper justice. This cannot be achieved in a society where the concept of jaat/jati
(loosely termed ‗caste‘) exists. So the annihilation of caste (and anything that supports the caste
system) becomes an Ambedkarite‘s priority number one.
I hope that answers the question asked

BBC NEWS (HINDI) Video exposes the Manusmriti:

The cruel punishments for violating the inhumane laws of Manu were mainly directed towards
women and the Shudras, depriving them of the most basic human rights. Many extreme rightwing religious fundamentalist are attempting the re introduction of the Manusmriti with the aim
of replacing the current Indian constitution with this anti humanity law book.

WHY did the Brahmin, GANGADHAR NEELKANTH SAHASRABUDDHE, put the
Manusmriti to ashes ?
Answer: Because it contains hundreds (if not thousands) of verses that encourage anti humanity
behaviour, especially towards women.
On 25th December 1927 at 9PM Dr Ambedkar participated in the public burning of the
Manusmriti at the hands of a Brahmin, Bapusahib Sahastrabuddhe.
This has now become a public event known as ―Manusmriti Dahan Day‖ and ―Istree Mukti
Divas‖ or “(Indian) Women‟s Freedom Day” but is not highlighted by the Indian authorities.
SOME QUOTES FROM THE MANUSMRITI:
(11 & 12 are from other Brahmanic religious texts that back the Manusmriti) :

1. If a person of lower caste adopts the occupation of a higher caste, the king ought to deprivehim of all his property and expel him from his kingdom. (Manusmriti, X: 96)
2. If a Shudra (lowest caste member) dares to give moral lessons to a Brahmin, the king is to gethim punished by pouring hot oil in his ear and mouth. (Manusmriti, VII: 272)
3. Similarly, if a Shudra occupies the same seat as a Brahmin, he is to be punished by brandinghis waist (with hot rod) or getting his buttocks cut! (Manusmriti, VIII: 281)
4. Even if the husband is morally degraded, engaged in an affair with another woman and isdevoid of knowledge and other qualities, the wife must treat him like a god. (Manusmriti, V:154)
5. Women should never be allowed by their guardians to act independently (Manusmriti, IX: 2)
6. If a person of lower varna (& lower caste) has sexual relations with a woman of higher varna,with or without her consent, he is to be killed. (Manusmriti, VIII: 366)
7. If a Brahmin (highest Varna) abuses a Shudra (lowest varna), he is to be fined mildly, but if aShudra abuses a Brahmin, he is to be killed. (Manusmriti, VIII: 267/268)
8. If a Brahmin kills a Shudra , he is to perform penance by killing a cat, frog, owl or crow, etc.(Manusmriti, XI: 131)
9. Non-believers, including freethinkers, rationalists and Buddhists, are not to be entertainedrespectfully as guests; though, mercifully, they may be given food (Manusmriti, MS IV: 30)
10. The families of non-believers are destroyed sooner than later. (Manusmriti, MS III: 65)
11. If a woman should not grant her man his desire, he should bribe her. If she still does not grant him his desire, he should hit her with a stick or with his hand, and overcome her, saying: ‘With power, with glory I take away your glory!’ Thus she becomes inglorious. (Brihadaranyaka Upanishad 6.4.7)
12. It is the highest duty of the woman to burn herself after her husband. (Brahma Purana 80.75)
13. When a woman, proud of her relations [or abilities] deceives her husband (with another man), then the king should [ensure that] she be torn apart by dogs in place much frequented by people and the evil man should be burnt in a bed of red-hot iron. (Manusmriti, MS VIII: 371/372)
14. Offering presents (to a woman), romping (with her), touching her ornaments and dress, sitting with her on a bed, all these acts are considered adulterous acts. (Manusmriti, MS VIII: 357)

There is more, a lot more ..