Radagast seemed to be an "animal whisperer", so what exactly was his point among the Maiar who were sent to guide the sentient races of Middle Earth to fight Sauron?
Radagast's mission was the same as that of the other Istari - to encourage resistance to Sauron, by various means such as coordination of the powers of the Elves against him through the White Council, encouragement of vigilance of Gondor and Rohan, or the removal of dragons that could prove a threat and replacing them with Dwarves to neutralise an enemy stronghold.
Emissaries they were from Lords of the West, the Valar, who still took counsel for the governance of Middle-earth, and when the shadow of Sauron began first to stir again took this means of resisting him. ... their emissaries were forbidden to reveal themselves in forms of majesty, or to seek to rule the wills of Men and Elves by open display of power, but coming in shapes weak and humble were bidden to advise and persuade Men and Elves to good, and to seek to unite in love and understanding all those whom Sauron, should he come again, would endeavour to dominate and corrupt. - The Istari, Unfinished Tales
He was included by special request of Yavanna, his Vala:
The note ends with the statement that Curumo [Saruman] took Aiwendil [Radagast] because Yavanna begged him ... On another page of jottings clearly belonging to the same period it is said that "Curumo was obliged to take Aiwendil to please Yavanna wife of Aulë."
As Christopher Tolkien notes in Unfinished Tales, there is no indication why Yavanna wanted Radagast included:
There is no hint of an explanation of why Yavanna's evident desire that the Istari should include in their number one with particular love of the things of her making could only be achieved by imposing Radagast's company on Saruman; while the suggestion in the essay on the Istari (p.407) that in becoming enamoured of the wild creatures of Middle-earth Radagast neglected the purpose for which he was sent if perhaps not perfectly in accord with the idea of his being specially chosen by Yavanna.
However Radagast does none of these. He becomes too enamoured of the birds and beasts of Middle Earth. As a result Radagast neglects the task he was sent to do, resulting in failure.
Indeed, of all the Istari, one only remained faithful , and he was the last-comer (dlanod's note: Gandalf, not Radagast). For Radagast, the fourth, became enamoured of the many beasts and birds that dwelt in Middle-earth, and forsook Elves and Men, and spent his days among the wild creatures. Thus he got his name (which is in the tongue of Numenor of old, and signifies, it is said, "tender of beasts"). - The Istari, Unfinished Tales