How to calculate number of days between to dates exclude special days?

Well, there's no "common list of holidays". It depends on country (national, public holidays) and religion. See: National day - Wikipedia[^].


The easiest way to detect if current day is a holiday, is to define a list of them. Note that some holidays are dependent of Easter...

Sub Main

	Dim startDate As DateTime = New DateTime(2019,1,1)
	Dim ThisYear As List(Of KeyValuePair(Of DateTime, Boolean)) = Enumerable.Range(0, 365) _
		.Select(Function(x) New KeyValuePair(Of DateTime, Boolean)(startDate.AddDays(x), IsHoliday(startDate.AddDays(x)))) _
		.ToList()

	'list is ready to use...
	
End Sub

' Define other methods and classes here
Function Easter(lyear As Long) As DateTime
	Dim C As Long, N As Long, K As Long, i As Long, J As Long, L As Long, M As Long, D As Long
	
	C = lyear \ 100
	N = lyear - 19 * (lyear \ 19)
	K = (C - 17) \ 25
	i = C - C \ 4 - (C - K) \ 3 + 19 * N + 15
	i = i - 30 * (i \ 30)
	i = i - (i \ 28) * (1 - (i \ 28) * (29 \ (i + 1)) * ((21 - N) \ 11))
	J = lyear + lyear \ 4 + i + 2 - C + C \ 4
	J = J - 7 * (J \ 7)
	L = i - J
	M = 3 + (L + 40) \ 44
	D = L + 28 - 31 * (M \ 4)

    Return New DateTime(lyear, M, D)

End Function

Function IsHoliday(ByVal thisday As DateTime) As Boolean

	Dim holidays As List(Of DateTime) = New List(Of DateTime)
	holidays.Add(New DateTime(thisday.Year, 1, 1)) 'New Year
	holidays.Add(New DateTime(thisday.Year, 1, 6)) 'Epiphany holiday 
	holidays.Add(Easter(thisday.Year)) 'Easter
	holidays.Add(Easter(thisday.Year).AddDays(1)) 'Easter Monday
	holidays.Add(Easter(thisday.Year).AddDays(49)) 'Whit Monday (48 days after Easter)
	holidays.Add(New DateTime(thisday.Year, 5, 1)) '1 May Labour Day
	holidays.Add(New DateTime(thisday.Year, 5, 3)) 'Constitution of 3th May - polish National Holiday
	holidays.Add(Easter(thisday.Year).AddDays(60)) 'Corpus Christi
	holidays.Add(New DateTime(thisday.Year, 8, 15)) 'Assumption of Mary
	holidays.Add(New DateTime(thisday.Year, 11, 1)) 'All Saints Day
	holidays.Add(New DateTime(thisday.Year, 12, 25)) 'Christmas Day
	holidays.Add(New DateTime(thisday.Year, 12, 26)) 'a second day of Christmas
	
	Return holidays.Contains(thisday)

End Function

Note: Easter function looks ugly, but works pefect!