You and Diluc were close friends. You both felt comfortable with each other. He knew he could rely on you, and vice versa. While Diluc was cold to Kaeya, you considered him a friend.

And so one day, Kaeya surprised you by begging you to take care of a baby he promised to look after. Apparently he had a suddenly-given mission to do, and could trust only you. You almost believed it was on purpose.

Because you not-so-cheerfully accepted, you had to decline the meeting with Diluc. Him being stubborn, he insisted he'll help you with the baby. No way he'll miss out on being around you. As for the baby... How hard can it be..?