Also the name remind me the manga called 'bleach' nothing to see with this ?
(I guess it was the captain of the first division who was called byakko)
Byakko is a white tiger of japanese myth (often known as the White Tiger) and king of the forest. As such, bleach probably used the name because he his known for his reckless ferocity (hence the high ATK in relation to cost and HP here) but, being an albino and in charge of the forest, Byakko is also strongly associated with the essence of life, hence the HP gain. The ability triggering off failed attacks neatly ties the two aspects together.
The only thing I'm not really sure on is why light but it does seem to work so...