I agree with the above post. Another element to the controversy involved the method of bombing they used, which was scientific in nature. High explosives were used in the initial raids, breaking apart the structures. Some military memos relating to the attack plan included the words "combustible material" as a rationale for using HE in the first waves of bombers.
Next, in concentric circles starting at the outer ring of the city, incendiary bombs started fires which spread inward towards the center of the city as the bombings continued in ever more concentrated circles. As the fire grew, it drew air from outside the city towards the fire, which then fanned the flames hotter and spread it towards the center of the city. Some witnesses have said the winds were over 60 - 80 mph in Dresden once the fires got going. This is what is referred to as a "firestorm", and the equivalent was similar to an atomic bomb, both in the number of people that were killed (some estimates were over 100,000) and the ferocity of the destruction itself.
So some of the controversy stems from the idea that Dresden was a test subject, a practice dummy for the science of firebombing that would later be used in Japan.
Note that Dresden was a major rail hub and had industrial production related to war production, even though Goebbels claimed it was all for civilian production such as toothpaste. The raid was officially part of an effort to assist the advance of the Soviet Union, but mainly it was one of the last major cities of Germany to be attacked.
Churchill afterwards expressed regret at the bombing of Dresden. As it was stated the bombing was less than effective in hitting its targets, but this was a factor of the the entire bombing campaign in Europe.
The overall bombing campaign of German cities did not begin to impact German production until 1945, and did not have the precision or accuracy that was claimed to the public of the Western Allies and its major impact to the war was the erosion of the German airforce, at the cost of large numbers of allied pilots and a vast number of German civilians.
The destruction of synthetic fuel production and key bridges had transportation rail stock had more impact on German war production than the bombing of German cities. The Dresden bombing seems to have had relatively little impact on the outcome of the war at the cost of many casualties and cultural monuments.
Much of the re-evaluation of the effectiveness of Strategic bombing came after the war, but even with this new evaluation, strategic bombin in this style continued into the Korean and Vietnam wars, it was only more recently that precision bombing rather than carpet bombing became technologically feasible and civilian casualties greatly reduced, although by no means eliminated, are of an order of magnitude much smaller than in WW2, Korea and Vietnam.
The use of incediaries creating firestorms (a.k.a. firebombing) created not only vast areas of destruction, deaths were created not only by burning,but also suffocation as air was literally sucked into the fire.
German civilian casualty estimates have ranged fro 250,000 to more recent estimates of 25,000. The novel Slaugherhouse Five is about the events in the Dresden raid, drawn from the author Kurt Vonnegut being a survivor of the attack, being an American p.o.w. in Dresden at the time of the attack.
Those who say that the bombing of Dresden by the Allies (the US participated too) was not justified argue that the city was not a major military target. They also say that the bombing did not even try to attack the military targets that did exist in the city.
People argue that there were very few militarily important targets in the city. They say that the supposedly important targets were really not that important. They emphasize that the scale of the bombing was way beyond what would have been needed to destroy those targets.
In addition, they say that there were relevant targets that did not even get attacked. They mention things like an army barracks outside of town that was not bombed. They also mention that various bridges were not attacked, which casts doubt on the claim that the bombing was meant to keep military supplies from being moved out of Dresden.
Overall, then, those who think this bombing was unjustified say that the city lacked military significance and that the bombing did not really try to target those places that had any military significance. Instead, they say that it was just a needless act of destruction.