My dad watched a lecture recently, where the speaker said that the Titanic sunk due to a impact with the iceberg when the ship reversed off the ice shelf it was on and not the initial impact with the iceberg.
No, it was not. The Titanic scraped alongside an iceberg which punched holes in its hull in several places below its waterline, including holes in many of its watertight compartments, causing them to fill with water and the ship eventually to sink. As /u/panzerkampfwagen correctly says elsewhere in this thread, the ship's engines were reversed in an effort to slow the ship, but that was ineffective. The ship slowed, and hit the iceberg glancingly along its right side.
Scientists at the University of Missouri-Rolla (now Missouri University of Science & Technology) actually studied samples of the Titanic's steel and concluded that it was fairly brittle, especially under cold conditions, and could shatter easily. Their research is summarized below:
I've never seen it claimed that the Titanic reversed off the iceberg instead it was put into reverse to help with steering to dodge the iceberg, which obviously failed (coming to a stop after reversing took quite a long time). The impact itself was a glancing blow as the Titanic passed.
The Titanic was designed with a number of bulkheads that created separate watertight compartments that could be used to prevent water from filling up too much of the ship. Too much water = ship sinks. The problem was that the berg compromised too many of the watertight compartments.