The fight happened between the Jabberwock and the boy.
The Parent (Mom or Dad) celebrated the Boy's victory against the Jabberwock.
The Jabberwock's Head
The poem reads, " 'Beware the Jabberwock, my son! The jaws that bite, the claws that snatch! Beware the JubJub bird, and shun the frumious Bandersnatch!' "
The story states, "The Jabberwock, with eyes of flame, came whiffling through the tulgey wood, And burbled as it came!"
In the end the boy slain the the Jabberwock, cut off its head, and they celebrated its death. The story proves, " 'And hast thou slain the Jabberwock? Come to my arms, my beamish boy! O frabjous day! Callooh! Callay!' He chortled in his joy."