The Phillips curve implied a static relationship between inflation and unemployment. Friedman and Phelps argued that this relationship was spurious. Why, then, did the Phillips curve appear to fit the data so well?

The short-run Phillips curve shifts whenever expected inflation changes. It follows that the static Phillips curve fit the data well because expectations had not changed much.
Another explanation exists. If you look at the historical graphs in the transparencies, you will see that the Phillips curve did appear to have shifted around before 1968. Most notable is the behavior of inflation and unemployment during the Great Depression. So one reason that the static Phillips curve appeared to fit so well is that economists and policymakers wanted it to fit. Recall that economists had a ready interpretation for the static Phillips curve: when unemployment is low wages get bid up and when it is high wages get bid down. Policymakers also liked it: it suggested they could choose a balance between inflation and unemployment according to their preferences. Put another way, economists ignored evidence that the Phillips curve shifted around. They attributed this shifting to the random noise associated with any economic relationship, rather than worry that it might have reflected some fundamental misspecification of the curve.