Why was Manny happy to be home in Parrot in the Oven?What experiences did he learn from?

Manny has come to the realization of whom he is, and what is important in his life.  While chasing after Eddie, the gang member who has just snatched a lady's purse, he experiences an epiphany.  Recognizing Eddie as the guy who hurt his sister, it was as if Manny had

"finally seen (his) own face and recognized (himself)...recognized who (he) really should be...(Manny) didn't feel like catching up to Eddie anymore...instead, (he) wanted to grab him, and scold him about how to treat people, how to be somebody who knows how to treat people".

Having realized this, Manny wants nothing more than to return to the security of the place that has made him whom he is - home.

Manny has learned many lessons from his experiences in the book.  Through the incident where he almost shoots his little sister when he is playing around with a gun, he realizes how quickly violence can destroy that which is dear to him, and from seeing Lencho lose both a fight and the respect of his friends, he discovers that being tough is not everything.  From his experience with the receptionist at the hospital who scornesHispanics and treats them like dirt, and the black man who helps him escape trouble when he is running away after the purse snatching, because the man distrusts white authority, Manny learns that prejudice is everywhere, and it is not always directed solely at him.  And after being humiliated at a white girl's party, and then allowing himself to be jumped into a gang so that he can get a girl, Manny learns that the acceptance of others is not all it is cracked up to be.

Manny is a young man with a good character and a strong sense of decency.  He finally realizes that he would not be happy being any other way when he recognizes that if he does not change his life he could easily become like Eddie, angry, unprincipled, and aimless.  He hurries home, where he finds his sisters lying asleep "on opposite sides of the couch", and he knows

"that (he'd) never again see anything so wondrous as his two sisters...the whole room...the squiggly TV, ...(his) mother's animals, gleaming in the sunlight...it was wondrous, like a place (he) was meant to be...a place...that (he) had come back to after a long journey of being away...(his) home".

In his moment of epiphany, Manny finally appreciates the value of the family which, despite their weaknesses, loves each other deeply.  He has learned what is important in life, and one gets the sense that, with the support of his family and home, Manny will continue to live, true to himself, and find a better life in the unforgiving world around him (Chapter 11).