I know exactly the reason okay here it is.
When you take steroids it puts strain on the heart, maybe even enlarging it slightly.
When you have local anaesthetic it similarly puts strain/pressure on the heart. Combining the two together potentially can be lethal and cause heart attacks and strokes.
Thats why ideally you should get your dentist work done with space either side of your cycle.
Anasthetic is harsh on your heart.