Since I've recently come across two people wrongly claiming otherwise - including one of my followers - I'm just going to set the record straight here: Ikem NEVER encouraged Ursa to give up her memories of Zuko and Azula in The Search.
The only time the option to have memories erased is ever bought up is when Ursa's speaking with the Mother of Faces. And it's the Mother of Faces who brings it up, when she senses that Ursa's desire for a new face by itself isn't going to fix her trauma over her life in the Fire Nation Royal Palace. Ikem never says a word during this conversation, and prior to the appearance of the Mother of Faces, he actually suggests trying to abscond with Zuko and Azula so that they, him and Ursa can live like a family together, before Ursa points out that this would ultimately cause Ozai to come after the four of them as well as their hometown.
If you want to hate the plot point of a mother being so traumatized by her past that she feels she's got no choice but to forget the traumatic part of her life in order to have a chance at moving on, whatever. But do your damn research and get the facts right beforehand, would you?
