I would agree that in removing a mole on the chin that only two layers of closure would be needed. My guess is that you and the first surgeon just had a misunderstanding about the closure. Perhaps she said you would need 3-4 sutures and not 3-4 layers. You might want to confirm this with her directly.
Typically, after removal of a soft tissue lesion in this area the resultant incision is closed in two layers. The deep dermal layer is first closed with absorbable sutures, followed by a tension free skin closure using permanent sutures which are removed in 7 days. Good Luck
The understanding of the layers of the skin and subcutaneous tissue needed to close depend on the depth of the wound, the anatomic layers, and the skin.
Wounds are closed to re-establish the normal anatomy