Seems a pretty large group of causes, as said, and not any one thing. The 'should have stopped, rather than keep moving' theory is probably the only nonsense one in the bunch. We've got:
-Dark, dangerous waters, going too fast. Slow down, ship is saved. Wanted to make headlines, plus thought ship was unsinkable, so no worries.
-Sideswiped iceberg rather than head-on collision. Biggest problem. Ship was designed to take a beating, but this was just past any planned spec. Ruptured too many compartments. Head on, you lose a couple in the front, and lots of people get hurt, but ship gets to New York just fine, but a little late.
-Too small rudder. Yeah, she was a big ol' bitch, and at the speed she was going, just not enough turning power.
-Too big a ship for crew. All experience was on smaller boats, this one didn't handle the same, and they didn't have enough time.
-Wrong orders. Should have let it hit head on, or put it in full reverse, or gone full steam and hard over, any of those would have worked. The new-ness of the ship worked against them, and they went hard over AND reverse, which didn't give them enough control to do jack shit.
-No ships in range for support, dumb route, thought flares were fireworks, can't exactly call 911 in 1912, etc. Shit was dangerous back then.
-Not enough lifeboats, poor planning. Ship can't sink though, and it looks dumb, so can't have that. That said, the available ones weren't filled, but you expect that kinda thing in an emergency. Blind panic does strange things to mobs...
Changing ANY of those things probably saves the ship. that ALL of them happened meant they never really had a chance...