I wanted to tell you something. I ... uh ... I really miss all of you, and the thought of never seeing you again sort of breaks my heart. So ... uh ... y'know, if you could, try to get in touch with me.
Those hardly sound like the words of a being who's happy to have escaped its dying planet. So that brings up an obvious question. Ask anyone who watched the show during its heyday and they will confirm, ALF was funny stuff. So ... what were we all laughing at? Maybe the answer to that question lies in ALF's adopted family, the Tanners, and their less than compassionate response to his arrival on Earth:
Willie: This is incredible, truly amazing, after all those years of wondering and hoping that it might be possible to contact alien life, to have this happen: It's a miracle. It's the fulfillment of a lifelong dream.
Kate: You've got to get rid of it.
Ha! That controlling shrew of a wife just never lets poor Willie keep the living, breathing, feeling alien life forms he finds lying around. Isn't that just like broads?
Unfortunately, the Tanners' dickishness in the face of a discovery that some argue could be the single event that unites mankind as one is also a trait that's present in their stupid jerk of a son. Check out his reaction to learning ALF's "funny" real name.
Brian: Your name's really Gordon?
ALF: Yeah, Gordon.
Brian: That's funny.
ALF: It was my mother's maiden name, all right?
And guess what: Despite this conversation, the Tanners steadfastly refuse to call ALF by his proper name, instead sticking with the generic acronym that translates to "alien life form." Hell, even the cat gets a proper name in the Tanner home, because an animal that's incapable of human thought or emotion is far more worthy of a personal connection than the thing living in your house that is for all intents and purposes a person who just happens to have a shit ton of hair.
There are other ways to handle that type of thing.