I lifted this great quote from Per Crucem ad Lucem which is from Anthony Robinson here on why 'family' is not a great self-designation for a church.

‘Many of the congregations that claim “We’re a family,” lose sight of larger transformative purposes and settle, instead, for the comfort and satisfaction of their members. The core purpose of a congregation – growing people of faith and helping people and communities move from despair to hope – gives way to lesser and even contrary purposes like keeping people happy. While it may not be a necessary outcome of the use of the family image, many congregations that gravitate towards it seem to make member comfort and satisfaction their de facto purpose.

That may be because “family” suggests to people something like, “We’re all loving and nice here.” That in turn often means no hard questions are asked and no honest challenges are allowed. It wouldn’t be nice.

I can think of other reasons to be cautious about “family” as our image for church. Families sometimes keep secrets that shouldn’t be kept in order to keep from bringing shame on the family name. And families aren’t typically that easy to join. Two of our sons were married in recent years. Turns out that putting families together is a fairly complex dance.

One last issue. The use of the term “family,” may communicate to people who are not married or to the married without children that they don’t quite fit. “Our church is a family,” morphs into “our church is for families.”

Keeping the family members happy, having everyone know everyone else and get along like “a happy family,” isn’t really the point for Christian congregations. Their goal and purpose is both different and higher.

Perhaps other biblical images like “People of God,” “Creation of the Holy Spirit,” or “Body of Christ” are better ecclesiological images? It’s not that these images don’t also have potential pitfalls. It is the case, however, that unlike “family” they are uncommon enough that people seldom have their own set ideas about what they mean. In some congregations, I hear leaders address the congregation simply as “church.” That too seems promising, reminding the gathered community that they are the Church of Jesus Christ (and the building is not).

If we must use “family,” we should be aware of the way that Jesus, while using “family,” also subverts conventional understandings of family and challenges their usual boundaries with a thoroughly new vision of “family.”’