If your mouse click is too sensitive, you may be inadvertently double clicking on a measure, which would select the entire stack.  

Thanks for the comment.  I figured out what is causing the issue and it's related to another issue that I posted about last week.  I think you might have commented on that too..    I am importing midi files into Finale and Finale is not cooperating very well with it.  It stacks staves even if I manually enter the slot numbers for the staves.  To go around it, I'm setting up a new file in Setup Wizard and copying and pasting the parts into the new file.  Finale was completely confused by the stacked staves (understandably!) and it was therefore selecting the whole bracketed family of instruments.  In this case all the woodwinds.  

The rest of the copying and pasting went fine and I just had to manually enter the stacked staff in.  This situation is not ideal, but I'm on a deadline and hopefully I'll fix it when I have more time.