Many reasons:
It was full. ALL of the landing and take off slots were full up, so it was filled to capacity this strangled trade and tourism.
It was dangerous, the Kai Tak landing required special training to land due to the mountains around HK look at videos on youtube. Even taking off was iffy as the end of the runway was sinking, you would hear the engines splutter on take off due to water splashing into the engines it was that bad.
As part of #2 with Kai Tak gone Kowloon land was freed up. With Kai Tak nothing on the approach to Kai Tak could be built more than 14 stories high. Once the landing flight path was gone buildings could pop up at any number of floors.
Kaitak's land itself was also freed up for residential buildings to ease the uber overcrowding of HK.
Pork barrelling. The HK economy was great in the 1980s and 1990s, they simply could not take the money away as the PRC and HK people would hate them for this. So the colonial government built a massive airport bring in expensive British contractors to do much of the work. Therefore funnelling much of the surpluses of HK into British pockets.