What is the context in which 'ice breaking' is a good thing?

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?

Solution 1:

In quite a few places throughout the world, transportation by water is an economic necessity.

In those areas that have a cold climate, that water often freezes in winter, making transport by ship impossible.

Specialized ships with reinforced bows can often be used to break that ice and make it possible for normal ships to use the waterways again, enabling transportation of goods and people, as well as communication with the outside world.

In that case, breaking the ice is breaking the "walls" that block you from the outside world.

Hence you should understand the use of "breaking the ice" in social interaction. An icebreaker enables you to comfortably get within someone's personal space and from that moment, communication is much easier.

Solution 2:

An ngram search discloses numerous uses of the phrase breaking the ice going back to the late 16th century, most referring to navigation, as suggested by oerkelens.

The earliest example I have found to date meaning to advance a relationship dates to 1594 (possibly 1591) in Samuel Daniel's Sonnet XLIII to Delia

When shall my faith that happiness attain,

To break the ice, that hath congealed her heart?

Samuel Daniel Delia 1594

Numerous examples appear in the 17th and 18th century publications meaning to thaw relations or get past personal, social, or political obstacles.