The parent-child relationship in Fahrenheit 451 is not a literal one, but a metaphorical one; Montag says that she makes him feel "very much like a father." However, the coming-of-age is not hers, but his; he has spent all his life accepting the world as it has been presented by society, and never thought to question it. Through Clarisse, he is able to view society from the outside:
"Have you ever smelled old leaves? Don't they smell like cinnamon? Here. Smell."
"Why, yes, it is like cinnamon in a way."
She looked at him with her clear dark eyes. "You always seem shocked."
"It's just I haven't had time--"
(Bradbury, Fahrenheit 451, Google Books)
These small stimuli are what spurs his change from an unthinking member of the collective society to an individual, reasoning instead of blindly accepting. Clarisse acts as the "parent" -- Montag even says that she sounds "old," showing that he is still young (undeveloped) in his own mind. By focusing on life through her eyes, Montag "comes of age" mentally, realizing how flat and unexceptional life in society really is.