Responses
Alicia asked Ares to pretend they are engaged in front of Kai because of the hit piece saying she was seen with her protege Noel (I think Kai's other sister did this).
She knows Kai is fangirling for Ares so he might accept him in a "relationship" with his sister and that it will also stop the rumors against her.

when exactly did they get engaged again?? and when did they actually start officially dating each other? i've been reading a bunch of manga/manhwa at the same time amidst other things and i think i'm losing track of what's been happening here