Watch that scene again. Rose climbs onto the door, but when Jack follows, it sinks due to the added weight. Clearly, only one of them could use it, so Jack selflessly let Rose have it. It was only later, when Jack realized he'd probably die from the cold, that he says his final goodbyes.
The thing I never understood about the film is an unseen plothole which could have prevented that could have saved Jack. Think back to the scene where Rose is being loaded in the lifeboat, she jumps out to stay with Jack. That begins a series of events which actually harmed Jack chances at surviving. Here's how.
Now think back, if Rose had just gotten on the boat and stayed in the first place, Cal would have likely just abandoned on deck and managed to get off with the Murdock character, who he briber. I know you'll remember this. Or he would have forgotten about Jack upon getting into the collapsable which he drifted off deck later. Jack would have had been forced to the stern with the other passengers and stayed until the rest of the ship went under the water, like in the movie right?
Now, remember that Jack found the
wall, not door when he and Rose are in the water with hundreds of other people. By the way it italiisized because it's the piece of wood from the grand staircase, you know in the dining room?
Look familiar?
He tells Rose where it is in the film. Now think, since he was the one to find the wall, he would have stayed on it while the rest of the people died around him. He could have waited for the only boat to come back to return and he could have been pulled from the water as Rose was.
Since both Cal, Rose, and Jack are all on different lifeboats, Rose and Jack could have reunited on
Carpathia, the rescue ship, and snuck away as Rose did in the film. Anyone notice that whole gap in fate that could have been? LOL