Why they became Animagus

'Now, my three friends could hardly fail to notice that I disappeared one a month I made up all sorts of stories. I told them my mother was ill, and that I had to go home to see her... I was terrified they would desert me the moment they found out what I was. but of course, the, like you, Hermione, worked out the truth...
'And they didn't desert me at all. Instead they did something for me that would make my transformations not only bearable, but the best times of my life. They became Animagi.'
'My dad, too?' said Harry, astounded.
'Yes, indeed. It took them the best part of three years to work out how to do it. Your father and Sirius here were the cleverest students in the school, and lucky they were, because the Animagus transformation can go horribly wrong - one reason the Ministry keeps a close watch on those attempting to do it. Peter needed all the help he could get from James and Sirius. Finally, in our fifth year, they managed it. They could each turn into a different animal at will.'
'They couldn't keep me company as humans, so they kept me company as animals. A werewolf is only a danger to people. They sneaked out of the castle every month under James's Invisibility Cloak. They transformed... Peter, as the smallest, could slip beneath the Willow's attacking branches and touch the knot that freezes it. They would then slip down the tunnel and join me. Under their influence, I became less dangerous. My body was still wolfish, but my mind seemed to become less so while I was with them.'