"I don't know why" could mean a number of things:
The answer is something that will make my parent annoyed if I'm honest.
It's not an outright lie to say "I don't know", but it's a dodge to avoid lying or having to instead confess to something worse. Like, "I didn't pick up my laundry when you asked me to because I was eating a donut after you said not to, and I couldn't come out of the kitchen with donut all over my face or you would know I ate it." This tends to be the least likely option, though, and also tends to be accompanied by guilty looks and/or other evidence of breaking the rules (e.g., fewer donuts in the box).
It could also be that he doesn't want to say "I didn't want to do what you asked, so I ignored it." (Would you react warmly and cheerfully to that, even as honest as it is? I wouldn't.) Even without a punishment attached, kids don't really want disapproval and disappointment, either.
I don't remember what I was thinking when I decided to disregard instructions,
or I don't remember being asked to do something.
In this case, he could say "I forgot what you asked me to do" but may be looking for a reason for why he forgot -- and the "why" of memory and attention is a complicated question!
My ten-year-old with ADHD has absolutely no idea why he has a harder time concentrating on instructions than most people. This frustrates him and frustrates me, so we both work on not looking for the "why" in those cases. (This doesn't imply your child has ADHD, neurotypical children also have moments where they're not paying attention. However, they won't have any better idea of why they weren't paying attention.)
I don't have a way to communicate the complex emotions behind my decision.
If I'm angry about something at work, I'm more prone to forget to run an errand on the way home that I need to get done. The distraction of all the other things in my life got in the way of doing what needed to get done.
But if somebody asks me why I didn't buy bread from the store, I would be hard pressed to explain the sequence of bad meetings, co-worker rudeness, and random software glitches that led to me being so frazzled. At best, I'd be able to say, "Ugh, I just had a bad day."
I don't want to talk about it.
This is a bit more common with older children, especially once you're hitting adolescence, but happens at pretty much any age. If they don't want to discuss what is going on in their head, this keeps that discussion from even starting. And the root cause of that could be any combination of the previous reasons, or wanting privacy, or feeling ashamed of themselves, or just not wanting to talk. (My kids know that any discussion about their motivations will lead to a discussion about making better choices, etc. and that can be boring/exhausting for them...)
Or, it's pure honesty: I don't know why I didn't want to do that thing.
Motivation is a complex subject, and even adults struggle to get to the root cause of choices they make. Sometimes people make bad choices, and children are still developing both impulse control and introspection.