I think this is what you're talking about. Please test on a COPY of your worksheet/workbook before running it on the real data to make sure it is, in fact, what you want.
Code:
Sub test()
Dim Col As String
Dim LR As Long
Dim i As Long
Col = "A"
LR = Cells(Rows.Count, Col).End(xlUp).Row
For i = LR To 1 Step -1
On Error Resume Next
If Cells(i, Col).Value - Cells(i - 1, Col).Value > 1 Then
On Error GoTo 0
Cells(i, Col).EntireRow.Insert
End If
Next i
End Sub
I started with this:
Excel 2013/2016
<colgroup><col style="width: 25pxpx"><col></colgroup><thead>
</thead><tbody>
[TD="align: center"]2[/TD]
[TD="align: right"]6/4/2018[/TD]
[TD="align: center"]3[/TD]
[TD="align: right"]6/5/2018[/TD]
[TD="align: center"]4[/TD]
[TD="align: right"]6/6/2018[/TD]
[TD="align: center"]5[/TD]
[TD="align: right"]6/7/2018[/TD]
[TD="align: center"]6[/TD]
[TD="align: right"]6/8/2018[/TD]
[TD="align: center"]7[/TD]
[TD="align: right"]6/11/2018[/TD]
[TD="align: center"]8[/TD]
[TD="align: right"]6/12/2018[/TD]
[TD="align: center"]9[/TD]
[TD="align: right"]6/13/2018[/TD]
[TD="align: center"]10[/TD]
[TD="align: right"]6/14/2018[/TD]
[TD="align: center"]11[/TD]
[TD="align: right"]6/15/2018[/TD]
[TD="align: center"]12[/TD]
[TD="align: right"]6/18/2018[/TD]
</tbody>
Sheet1
and ended with this:
Excel 2013/2016
<colgroup><col style="width: 25pxpx"><col></colgroup><thead>
</thead><tbody>
[TD="align: center"]3[/TD]
[TD="align: right"][/TD]
[TD="align: center"]4[/TD]
[TD="align: right"]6/4/2018[/TD]
[TD="align: center"]5[/TD]
[TD="align: right"]6/5/2018[/TD]
[TD="align: center"]6[/TD]
[TD="align: right"]6/6/2018[/TD]
[TD="align: center"]7[/TD]
[TD="align: right"]6/7/2018[/TD]
[TD="align: center"]8[/TD]
[TD="align: right"]6/8/2018[/TD]
[TD="align: center"]9[/TD]
[TD="align: right"][/TD]
[TD="align: center"]10[/TD]
[TD="align: right"]6/11/2018[/TD]
[TD="align: center"]11[/TD]
[TD="align: right"]6/12/2018[/TD]
[TD="align: center"]12[/TD]
[TD="align: right"]6/13/2018[/TD]
[TD="align: center"]13[/TD]
[TD="align: right"]6/14/2018[/TD]
[TD="align: center"]14[/TD]
[TD="align: right"]6/15/2018[/TD]
[TD="align: center"]15[/TD]
[TD="align: right"][/TD]
[TD="align: center"]16[/TD]
[TD="align: right"]6/18/2018[/TD]
</tbody>
Sheet1
This is assuming saturdays and sundays (or at least one or the other) are missing from your list of date. If you have continuous dates all the way down, that particular code wont work.