It changes risk decisions: instead of worrying only about safety the pilots/operators start to also worry about making the schedule. In the history of aviation, it led to numerous accidents and incidents of pilots flying into bad weather, pilots flying un-airworthy aircrafts, etc. only because they've had schedule to meet.

Safety loses out when you're on a deadline.

I flew private with someone when I was a student pilot; we were on a deadline, so instead of waiting for the weather to let up, we were scud running about 300 miles back to our home airport (http://en.wikipedia.org/wiki/Scud_running). This is inadvisable; you're throwing minimum ceilings out the window, and hoping you don't run into obstacles on the ground (wind towers, cell towers, antenna guy wires).

It's not just dangerous, but illegal if you get caught. (Note: I was not PIC, and did not make the call). Do not do this.

EDIT: /u/lsh123 said it better.