One possibility is that they do not wish to take part in the matter at hand and come up with a quick explanation of their inadequacy relating to the matter, effectively making the other person dismiss him. I find myself unwilling to believe this, since it would effectively mean that the person is understating his abilities just to get away from something that is probably highly meaningless to him anyways. Perhaps if the person has a low self-esteem or doesn't really care what the other person thinks about him, presenting one's abilities in this way would be understandable. Still, that's only a minor part of people.
The second, most obvious reason would be that the person simply isn't good with whatever it is you asked him. But is that a reason to refrain from trying? Normally, no. While it is perfectly understandable for a person to work his way out of a situation where actual losses are possible by stating his limited ability as something could be permanently damaged, this is rarely the the case. Oftentimes the only loss anyone could suffer is the person's self-esteem as the response he'd give would not satisfy the questioner, and even in these cases any actual loss is highly questionable, as by escaping a matter by saying "I'm not that good with it." would just lead to the same loss. Is the false protection of one's self-esteem truly a reason enough not to take the chance of producing something that'd be useful? For me, it's a reason but not a good one.
This submissive way of performing tells to us that people are so instinctively afraid of failure that when presented with a low-gain situation where they think they can lose something, they refuse to take part it. One can easily see where this approach leads when applied to other decision-maked processes, and through that see the how it's inherently flawed. Next time you face a similar situation, think "What can I really lose by trying?" In most cases it's nothing, so go ahead and give what you can even though you may not think it's sufficient.
