Family may mean a blood you have,including the environment in which you live,including father,mother,sister or brother,including distant relatives.
It might not have meant either.
It may mean the blood and people that you care.
when you said about a family, it must be meant blood and who you care because it is one thing in your life that you meet in everyday. Instead, we must consider the relationship among the family member.
In this speech, the family means friend, relationship between relatives and your pet