You can use AUTOFILTER for things like this. This should get you there, or close enough for you to finish:

Option Explicit

Sub FilterOutFALSE()
Dim LR As Long

With ActiveSheet
    .AutoFilterMode = False
    .Rows(1).AutoFilter 3, "False"
    LR = .Range("A" & .Rows.Count).End(xlUp).Row
    If LR > 1 Then .Range("A2:A" & LR).Value = ""
    .AutoFilterMode = False
End With
    
End Sub