Why Lord Vishnu took Matsya avatar

 Lord Vishnu had pledged that he would appear every time someone threatens the existence of humanity. He had vowed that he would take an avatar on earth to restore Dharma by uprooting Adharma.

Once there lived a demon named Hayagriva. He was the son of Sage Kashyapa and his wife, Danu. People hailed sage Kashyapa for being a boon to humanity, but Hayagriva was the exact opposite. The demon was chosen as the Danav Raj (king of the demons). And his sole motive was to stop the humans from becoming more powerful than the Danavs.

Hayagriva wanted to establish the Danav clan as the most superior one. Therefore, he made several attempts to disrupt the progress of the human class. And after learning that Lord Vishnu had handover the four Vedas to Lord Brahma, he decided to steal them to stop the sacred texts from reaching the humans.

Hayagriva succeeded in stealing Rig Veda, Yajur Veda, Sama Veda and Atharva Veda from Brahmaloka. 

Brahma knew that the people on earth will not be able to make use of the Vedas until they are purified. He knew that social values had degenerated, and hence, the need for reestablishing humanity had risen. Therefore, he sought help from Shiva to destroy humanity only to produce a conducive atmosphere for a revival of the human race.

Vishnu knew about Shiva's plan to cause massive floods. Therefore, he incarnated in the form of Matsya (a fish). Moreover, he had to save Manu and his wife Shatarupa, the couple that would be instrumental in conceiving humans once again.

Hence, after killing Hayagriva and retrieving the Vedas, the Matsya avatar of Vishnu saved Manu, Shatarupa, the Saptarishis (who represented knowledge) and one set of each of the other living beings. In the end, he handed over the Vedas to Manu so that he could use them for the welfare of humankind.

Matsya may be depicted either in animal form or in a combined human-animal form, with the man as the upper half and the fish as the lower half. Matsya is generally represented with four hands—one holding the conch shell, one holding the discus (chakra), one in the pose of conferring a boon (varada mudra), and one in the protection-affording pose (abhaya mudra).