In response to your basic question, the government has to inject seasonal adjustments into the report, otherwise the numbers would be meaningless. What’s important is not the absolute number of added workers or subtracted workers, but the change relative to an average of past years for that month. Only then can we discern an underlying improvement or decline.
It also happens for other data the government reports, such as retail sales. Say you are a store that typically does $120 million in sales per year. On average you do $8 million per month for eleven months, then $22 million in December, for the $120 total. If last December you did only $15 million, would you be happy because it is above your monthly average? Seasonally adjusted, that December would be considered an awful month, as it should be.
The tricky thing the government must do is adjust for many such seasonal influences that are often changing over the years, and it is often unfairly blamed unfairly for getting it wrong or making the change late. But they revise their methodology when warranted, and I’ve never seen conclusive proof they are tilting the numbers. Their assumptions and definitions are there for everyone to see and analyze, their footnotes and addendums explain everything, and attacks by the out-of-power political party, both Democrat and Republican, are routine.
