Why didn't the passengers and crew of the titanic take refuge on the iceberg that they hit?

The titanic didn’t hit the iceberg and stop; it continued moving. By the time they realized the ship would sink, the iceberg was no longer in view.

The answer above about the ship moving past the berg is correct. The ship was very hard to steer as it didn’t have a long enough rudder and nothing that big moving that fast in water is easy to stop, either.

Most of an iceberg is underwater. The most damage done to Titanic was underwater. And I don’t know how you would move a ship that weighed tens of thousands of tons up onto an iceberg.

Yeah.
And why did Leo DiCaprio boycott the Oscars, just because he wasn’t nominated ?
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Here’s an interesting photo some people think is the iceberg that sunk the Titanic.

Even if the ship stayed close, how easy could it be to climb onto an iceberg?

I do not think many of those people would have been able to get a good grip on the thing, actually cling to it, then climb up it to safety. And that would only apply if the ship has stopped when it hit the iceberg which didn’t happen anyhow.

@Supacase I was thinking the same thing. Assuming (and it may well be) that was the actual iceberg (in bkcunningham’s link) which sunk the Titanic, that chunk of ice looks very steep. Some speculate that the Titanic’s name was switched with the Olympic, and supposedly it’s bad luck to rename a boat.