With an increased number of computers doing people's jobs in fields like manufacturing, there's an increased number of people required to maintain those systems. Programmers have to make the programs, people have to design the actual machines that do the manufacturing, and more. These are all full-time positions.
In addition, computers are there to make the job simpler and less tedious - not the replace human workers entirely. This is especially true in office-related positions. Take, for instance, advertising - before computers with graphics design tools like Photoshop, the people doing design would have to spend a lot more time and effort to manually cut out certain sizes of pictures, glue them together, paint, draw, and more. Nowadays you can replace all of the tools you would use to do that with a computer and printer. While this means the employee can get the job done faster and in an easier manner, the fact that computers can't design advertisements on their own means they are not a threat to a graphics designer's job (unless another graphics designer who knows the software better is looking for the same position which is not part of the argument here). Moreover, because of this increased efficiency, the same graphics designer can accomplish much more in one day than before. Businesses don't have a fixed amount of work that needs to be done - if they have the resources to do more but are not using up all those resources, be they human or material, they will try to expand so that all the resources are used up or lay off and cut down on how many resources they have. It's simple economics.
On the topic of reliance on computers (in response to c3barkho, the con side, c7muisec):
In any technology new or old reliability and durability are both issues. For example ink can fade and stone can erode. With regards to the Comair example, the computers were what enabled the airline to schedule the 1,100 flights to begin with, therefore though the system had failed in that one case the beneficial work which the computers had provided beforehand and afterward far outweigh any single instance of malfunction.