Personal tax is just that. Personal.
This is not so much about taxes, but more about social security payments (healthcare, pension, unemployment). In Germany, these must be paid, at least in part, by the employer. The rules forbid that a self employed "contractor" works full time for a single client (with some rare exceptions, but "airline pilot" is not among these).
What this airline is doing by not employing their pilots directly but contracting them as individual sub-contractors is called "Scheinselbständigkeit" (something like "pretended independence") and this is what the authorities are after. In case the authorities win their case, the airline will have to pay social security for all their pilots in Germany for up to four years retroactive.