You cannot use 'Selection' in this way to format the header footer as the header footer is not selected. You need to work with the range as you already began to do.
Using separate passwords depending on the content of the dropdown is fraught with problems. It relies on the user selecting only the dropdown entry that relates to the password, so in that case why have a dropdown at all - if you can only make one usable selection?. The following code has a common password (and reprotects the document with that password after processing the entry).
If you have the values in the dropdown that you want in the header and footer, there is no real need for the macro. You can use REF or STYLEREF fields instead and avoid the need for macros in a form which you are presumably going to distribute. However given that you are learning VBA, the following should work for you

Sub SetHeadersFooters()
Dim oRng As Range
Dim sPassword As String
Dim strHeading As String
Dim i As Long
    sPassword = "topics" 'Use a common password
    If Not ActiveDocument.ProtectionType = wdNoProtection Then
        ActiveDocument.Unprotect Password:=sPassword
    End If
    Select Case ActiveDocument.FormFields("ddsubject").Result
        Case "MATH": strHeading = "MATHEMATICS"
        Case "ENGLISH": strHeading = "ENGLISH"
    End Select

    For i = 1 To ActiveDocument.Sections.Count
        With ActiveDocument.Sections(i)
            'process the headers
            Set oRng = .Headers(wdHeaderFooterPrimary).Range
            oRng.Text = "SUBJECT: "    'enter the common range text
            oRng.Collapse 0    'collapse the range to its end
            oRng.Text = strHeading    'add the variable text
            oRng.Font.ColorIndex = wdRed    'colour the variable text
            'Repeat for the footers
            Set oRng = .Footers(wdHeaderFooterPrimary).Range
            oRng.Text = "SUBJECT: "
            oRng.Collapse 0
            oRng.Text = strHeading
            oRng.Font.ColorIndex = wdRed
        End With
    Next
    ActiveDocument.Protect wdAllowOnlyFormFields, Password:=sPassword
End Sub