Professional or personal?

I've been struggling this week with the balance between the professional and the personal in meetings.  A professional meeting, that is, one that occurs on work time or in a work capacity, requires a more professional tone.  The meeting agenda stays focused on the agenda and tasks, rather than our personal feelings and needs.  A family meeting around the kitchen table, for example, that's where the personal shows up.  But this week I've experienced some meetings where the two got blended together.  That surely is unavoidable.  And I'm still trying to figure out the right blend.