During the investigation, it was discovered that a whole series of rules were violated to get the shuttle up in the air. Despite the engineer’s protests about the O-rings and fuel, NASA still proceeded with the mission – in direct violation of their set launch rules.
The supposed reason was to maintain the illusion that the space program was infallible. That the Regan Administration could maintain a fleet of spacecraft, launch them regularly and dominate the space race. A cancelled launch would have created doubt and potential funding issues.