it's probably not a literal meaning of 'can't live without'. Like, people say 'I can't live without my cup of coffee first thing in the morning'. They can, they just really like coffee. I guess it's the same with Farfetch'd. Also, he uses it to defend himself from would-be attackers, so in a sense it helps him to live, ergo, he could not live without it.
well maybe the fights are to the death and they fight to get sticks. it would explain a lot.
grandma farfetch'd to grandson farfetch'd, "If you dont straighten up ill get my bad stick on you!!!"