The monthly employment situation is two surveys published together. The payroll number comes from employers. The unemployment rate comes from households. They can disagree, and the disagreement is not a scandal. They ask different questions.
The first print of payrolls is revised. Twice, in the next two reports, and again in an annual benchmark. A sentence that treats the first print as final is already out of date by the following month. Read the level and the revision, not only the headline change.