You don’t need to tell me why you can’t meet at a specific time. In fact, I don’t want you to tell me why. Because the more you say and the longer your answer is the more it sounds like an excuse.
When someone requests specific time of me and I have a conflict, I tell them: “Sorry, I have a conflict at that time.” I don’t go on and on about the status of my family or the fullness of my calendar or seven other reasons why that time won’t work. I simply state that I have a conflict and ask if we can find another time.
I state my response simply and directly so I can get on with finding the next best solution. If I did start to tell you a story about how busy my week was and the unexpected events that happened, it would sound like an excuse. Or worse yet, that I was trying to show how important I am with all the meetings on my schedule.
So, save yourself the story and be honest. If the time doesn’t work, state that. But don’t tell me why. I don’t need to know and neither does anyone else.