The film is about divorce and the separation of family. It is about two outsiders, one from earth and one from another planet. They are each outsiders that find friendship in each other.
Elliot is a boy who is pushed on the outside by his brother, his school and his father has left his mother for another woman. E.T. represents every child's imaginary friend come true. The two characters become so close they even start sharing the same feelings. For Elliot, E.T. is the one thing that makes him special and he does not want to share E.T. with any adults. Elliot tells the man with keys "He came to me." The man with keys represents Elliot as a grown up. This is Elliot's coming of age scene where is becomes an adult. It is also represented by E.T.' resurrection. (Biblicatl reference). This represents the end of childhood and the begging of Elliot's Adulthood.
The change in Elliot is a parent as he now leads the other boys on an expedition to get ET home. Now, as an adult E.T. realizes he can't be selfish and have ET all to himself. He must set him free. Before Elliot tried making excuses, wanting E.T. to stay with him forever (A very childish approach).
E.T. also also shows us two characters from different cultures that find commonality in each other. The approach is not hostile. Adults are the only hostile ones in this world. Much of the time the camera angles are low and the threatening adults are seen from the waist down child's view (similar to the Charlie Brown parents). E.T. makes the children forget their petty differences, stop the teasing and bickering and touches their lives. E.T. is very much a symbol for a savior. He heals with his touch and teaches the children to be caring. (Not to mention he dies, comes back to life and returns to the sky (resurrection)).
I would argue this film is more of a fantasy tail than science fiction.
Dude. This movie is all one big allegory about the trials of GBLT rights. This movie's totally advocating for gay marriage.