There have been a number of similar questions here before, and the basic summary is that the designers and builders never said it was unsinkable. There is one reference to marketing material which says that the ship is DESIGNED to be unsinkable, not that it is. The Unsinkable was mostly generated up by newspapers at the time. It was the ship's number of bulkheads and electrically-sealing doors which were the unique aspects of its design which made it be deemed unsinkable.

There were some problems with the bulkheads, though. Mostly, they weren't watertight and weren't sealed at the top; therefore, if a particular bulkhead got filled with enough water, it would start spilling over into the next one.