This macro is designed to compare the data in column C and D and if C does not match D in a certain row, it deletes the entire tow. The problem is that it deletes the header
If you use a descriptive variable naming, eg. rename i into iRow you will never forget that this is your row counter, that is counting from row 9999 to row 1 in For iRow = 9999 To 1 Step -1. So you need to change the 1 into a 2 to omit the first row.
I recommend to use a dynamic start for your loop that automatically finds the last used row. This prevents unnecessary loop steps and you don't need to increase it for larger worksheets.
Option Explicit
Public Sub DeleteNonMatchingRows()
Dim LastRow As Long
LastRow = Cells(Rows.Count, "C").End(xlUp).Row 'find last used row in column C
Dim iRow As Long
For iRow = LastRow To 2 Step -1
If Range("C" & iRow) <> Range("D" & iRow) Then
'Range("C" & iRow).EntireRow.Delete
Rows(iRow).Delete 'directy delete a row
End If
Next iRow
End Sub