Firstly, accuser is probably the wrong word here altogether:
someone who imputes guilt or blame.
Accuser is a strong word, because it implies that the person is claiming that you are not only wrong, but also guilty or to blame for something (perhaps guilty of spreading falsehoods). Since you are claiming that they are wrong, you are accusing them of making false accusations, and hence a liar, which is a major insult.
Perhaps you want one of these words:
opponent (esp. in a formal debate scenario)
friend/colleague/student/person I met on the Internet (or any other relation)
You can even get away with avoiding the word altogether, since it's implied by the rest of the sentence anyway. Change the adjective inexpert to the noun non-expert and you have the sentence:
How can you explain to a non-expert that ...
But we can improve the sentence further by making it less abstract:
How can I explain to a non-expert that...
And you can even choose to be more polite by avoiding the implication that your opponent is not an expert (which sounds prima face that you are calling them an idiot, which is rude), by changing the emphasis on you needing an simple answer because they are unable to cope with a more complex one, to simply asking for a simple answer full stop:
How can I explain in a simple way that...