I was struck by the same questions when first learning about the Titanic, and it appears shocking, but has reasonable causes.

1. It took a while to assess the damage. Captain Smith, designer Thomas Andrews and various officers had to diagnose the problems. When they found the boiler rooms and mail room flooding, Thomas Andrews stated that the ship would last around an hour or hour and a half tops. It actually lasted two hours and twenty minutes, with this extension likely coming from efforts made by the ships engine crew pumping water out.

2. Nobody thought the ship would sink. Titanic was designed to be able to take on significant water and still stay afloat. This was due to compartmentalisation, meaning parts of the ship could flood but others would keep it bouyant. The idea was that Titanic should act as its own lifeboat, keeping people warm and safe until someone could pick up the passengers - far less dangerous than risking the lifeboats

The problem was that the iceberg pierced flooded five compartments, and Titanic could only afford to lose four. It was expecting to collide with ships close to head on, not mountains of ice bashed against its side.

When people were told to get up top, there was almost no panic, little evidence of damage and it was incredibly cold and late at night. Some people ignored the request, thinking nothing was seriously wrong and that it wasn't worth the effort of climbing multiple decks to go outside. Even some officers went back to sleep before being told the full extent of the disaster.

When the lifeboats were being loaded, many passengers refused to get in, thinking they were safer on board.

3. The crew were not fully trained on operating the lifeboats. They only performed one incredibly inadequate test before leaving Britain, and never drilled the passengers or practiced safety drills themselves. The lifeboats were not properly provisioned (eg. food), the crew didn't know which lifeboats they were assigned to, and many believed the boats would snap if overloaded with passengers (they had only recently been reinforced with steel). The davits (pulleys) were incredibly stiff because they were mostly unused, leading to difficulty in coordinated lowering, and the ship was listing and sinking unevenly, making getting in the boat awkward and dangerous.

I've also seen it argued that Captain Smith may have zoned out, giving vague orders and failing to lead in regards to the lifeboats. This may be true, but others commended his bravery in other aspects of the sinking.

4. They had difficulty finding passengers. As mentioned earlier, many passengers thought Titanic far safer than the lifeboats, even when sinking. On top of that, Captain Smith ordered Officers Lightoller and Murdoch to load "women and children first". Murdoch interpreted this to mean load all nearby female passengers, and then nearby men. Lightoller believed it to mean ALL female and child passengers first, then men.

Lightoller's decision may seem unreasonable now, but it was made under severe duress, and he was following orders. It was also perfectly acceptable to most men on board, who escorted women to the boats, helped them load, then often went off in search of more. This search for women delayed the loading.

He also ordered some men to open the gangway doors lower on the ship, and ordered those in the boats to stay by the ship to pick up more passengers, clearly aware that these boats were too empty. The crew who went down to the gangway doors never returned, the door unopened. Only two boats came back to the ship - some were told to head for lights in the distance, many feared the Titanic sucking their boats down, and most feared that they would be swamped by thousands of desperate swimmers. Captain Smith also shouted at the boats to come back through his megsphone. In most cases, the crewmen suggested going back but were shouted down by passengers.

Men were ordered out of some boats at gunpoint, and several survived only by jumping in the boats as they were lowered, injuring people and risking all of their lives. Most men who survived were let onto their boats by Murdoch after all nearby women were loaded.

5. Many passengers were trapped or lost below decks.This is especially the case for third class passengers - Titanic was enormous, so third class passengers were the last to find out about the iceberg and had the furthest to travel from the lowest decks to the top. A quartermaster even sat at attention for an hour of the sinking totally unaware of what was happening until he saw a boat in the water - he had to ring the bridge to find out they were sinking, despite being on deck. Many passengers became lost or trampled in the panic, trapped under sliding furniture or in dead-end corridors.

All this being said, the crew did their utmost and any complacency or failures on their part can be traced back to everybody, from the owners to the designers, to the passenger liner industry and even the passengers themselves. Nobody at all thought the Titanic could sink the way it did, and their complacency was generally born out of prior experiences. Lifeboats could be quite dangerous too.

The officers remained at their posts loading the boats even as the desperate rushed them and the ocean lapped at their knees. Murdoch and Smith died, despite having every chance to put themselves in boats, and Lightoller only survived by clinging to an upside down boat and taking charge of those who clung on with him.

Contrast this with recent shipwrecks like the Costa Concordia or Sewol Ferry, where the crew were the first to flee and left their passengers to die.

Two of the best books on the subject are Walter Lord's 'A Night To Remember' and 'The Night Lives On'. James Cameron's 1997 movie was based upon these books, and Lord served as a consultant.

There are multiple books written from passenger perspectives, and the British and American inquiries into the sinking also detail what went wrong and can be interesting reading.

OP mentioned animations of Titanic sinking. This is the best I have seen, as it includes the telegraph messages as well. https://www.youtube.com/watch?v=PGKpT1oGAnQ&list=LLhfLmOwmvMvgX0_PNAhxPwQ&index=6&t=0s

Here are two docudramas related to the sinking - one on the SS Californian, who were accused of failing to rescue the Titanic; and the other about the heroic efforts of the engine crew in running the pumps and keeping the lights on. https://www.youtube.com/watch?v=0RAckUr6KnM https://www.youtube.com/watch?v=3nhU11Y7u4s