Why were the FBI agents so willing to risk the hostages' lives?

Question

Throughout Die Hard it is clear that the two FBI agents on the scene, Johnson and Johnson, are more eager to fight the bad guys than rescuing the hostages. Their apathy for the hostages is most clear during their dialog on approach to Nakatomi tower:

BIG JOHNSON (shouting, to the pilot): Stay low. They're expecting transports, not gunships.

LITTLE JOHNSON (shouting over the noise of the rotors): What do you figure on breakage?

BIG JOHNSON: I figure we take out all the terrorists, and lose 20 percent of the hostages... 25, tops.

LITTLE JOHNSON: I can live with those numbers.

They were fully aware there were about thirty hostages in the building and that attacking in a gunship could cause the deaths of a quarter of them. Why would the pair be so willing to risk the lives of the hostages, especially as they were under the scrutiny of a live television broadcast?

Answer 1

This added to the film's overarching theme of John McClane having the deck stacked against him in every way imaginable.

The theme of Die Hard is that the protagonist prevails when virtually everything is going wrong for him. He shows up under-dressed to a party, makes a bad impression, botches his reunion with his wife, gets caught without even a pair of shoes on with nothing but his side arm against a group of 15 or 20 terrorists with automatic weapons. He manages to kill one and get his weapon... only to find that he just killed the brother of the most dangerous terrorist who is now out for blood (and also that his shoes are too small for John to wear).

One of the main threads of this theme is that the authorities – who should be there to support him – are not only unhelpful, they actually work counter to his effectively dealing with the terrorists. First we have Powell, who initially is going to leave the scene as a false alarm. Then we have the grossly incompetent LAPD commander and his SWAT commander, whom John has to save from their own bungling. Finally, the FBI arrives as the ultimate authority hurdle for John to have to deal with. First they play directly into the terrorists' hands by shutting off the power, then they nearly kill him with their gunships. The LAPD's unhelpfulness is born of incompetence, the FBI's is born of hubris and callousness.

The movie revels in John persistently hanging in there and prevailing against greater and greater (and more and more ludicrous) challenges from not just the terrorists, but from virtually everyone, including the hostages to a certain extent. Only John's wife and Officer Powell are actually competent and helpful, though they are mainly sidelined by other forces through most of it. The cartoonishly arrogant and cold blooded FBI agents are just one more part of this absurd puzzle. Like the "incompetent police," the "cocky and gun-happy FBI" is an old trope – one that dates back to the days of Prohibition when they had to go up against very well armed criminal organizations. It really isn't a fair trope, but it is one that is easy to fall back on when you need FBI agents to be a problem rather than a solution.

Answer 2

A little later on in the helicopter:

Just like Saigon, eh, Wally?

The "fall of Saigon" was thirteen years previously. This implies that the FBI agents had experience of the Vietnam war and its disregard for civilian casualties.

I've been looking for other historical events that this might be referencing and not come to firm conclusions. There were a number of high-profile anti-terrorist raids in the 1980s and 1970s (e.g. Entebbe), most of which had at least one civilian casualty. Gruber himself references a number of (fictionalised, but based on real groups) terrorist organisations in his speech of demands.