Humans' relationship with freedom is ironic. When they have it, they often take it for granted, willingly trading it for a more comfortable life. Yet, when they lose it, they yearn for it desperately, even to the point of risking their lives to reclaim it.
Ace had paid enough attention in history class to realize this. If he wanted to turn things around with Layla and get her to serve him willingly—enthusiastically even—he needed to make her believe it was her choice. It had to feel like she was doing it out of her own free will. Whether or not she realized she was Emi's Shikigami Slave didn't matter in the long run. Her life bond with Emi's Shikigami, her Curseling partner, would ensure she fulfilled her intended role.