If you are on a frozen lake and the ice breaks you basically plunge into cold water. That could end badly.
What is the explanation for 'getting to know everyone', or 'getting the conversation started' gets to be called 'breaking the ice', or any action that causes dialogue to start gets to be called 'icebreaker'?
There are other phrases like 'thawing of relations', or 'warming up to each other' which are used to describe people starting (starting again?) to get along. But is 'icebreaker' just a mistake that became popular and then accepted?