They are all okay, but they have shades of different meaning. "A/an/the" is a hard topic. There are some rules, but the use often depends on tradition or context.
Originally Posted by Csika
Here's my opinion:
When you say "the explanation" it is like you are implying that there is one, unique, pre-existing explanation that you don't want to give OR the idea of explaining in general is not necessary.
"An explanation" sounds less specific, like you have not tried to explain yet.
"Explanation" sounds like the activity of explaining as a topic. It sounds like "I don't want to spend time doing that activity."
A free email English guide!