Это будет то, что вы ожидаете
from datetime import datetime, timedelta
work_days = (datetime(day=31, month=1, year=2019) - datetime(day=1, month=1, year=2019)).days
empl_a = (datetime(day=1, month=1, year=2019), datetime(day=4, month=1, year=2019))
empl_b = (datetime(day=22, month=1, year=2019), datetime(day=25, month=1, year=2019))
empl_c = (datetime(day=10, month=1, year=2019), datetime(day=20, month=1, year=2019))
empl_d = (datetime(day=2, month=1, year=2019), datetime(day=6, month=1, year=2019))
total = sum((date2 - date1).days for date1, date2 in (empl_a, empl_b, empl_c, empl_d))
print(work_days - total)