In Your Opinion, Is This A Convincing Argument? Why Or Why Not?

I'm afraid that I have to agree with tiggersmom on this one, that it is not, in fact a convincing argument.
 To answer the rest of your question, the reason it is not convincing, is that the fact that the child pointed out the lack of chocolate stains means that most likely (very possibly previous experience) she knew that having chocolate stains on her hands would be solid proof of her having taken the cookies, and thus may have washed them to remove the 'evidence', then, having established in her mind a solid alibi, made sure to point it out.
 This does not necessarily lead to grounds of assumptive guilt, but is potentially suspicious, in that she uses it as her primary defense.
 I hope this helped in some way... Have a great day!

Well, in the child's eyes it is a convincing argument, but we as adults would know better. They don't have any real experience with debating something like that, so it would be infantile. Hope this helps.