I'm wondering if it's even worth the effort to explain or apologize to someone who's so impatient and possibly doesn't even have the room in themselves to understand. You did nothing wrong. And, if they did that once, it's likely they'll do it again, or be unreasonable with you in some other ways.
I know you would like for them to know why you didn't get right back with them. But, by blocking you, they may have saved you from other problems you might have had with them.
Fortunately, there are lots of other people who won't block you, no matter how long it takes for you to get back with them.