Yeah, there is the 'art is personal' aspect and it explains why people are insecure about what they draw/choose to portray/etc, but that doesn't really explain insecurity about skill. In that aspect, I feel like it has more to do with this:
Conversely as an artist, you wouldn't worry about your creation killing you, like a boat builder might.
Another aspect though might be that everyone can have an opinion on art. If you in, say, a super obscure and/or technical academic field, people can't really criticize you unless they're also well-versed in that field, but with art, even someone who can't draw themselves can tell when your anatomy is off, for instance. This means critics are less likely to have that empathy that comes from sharing your experiences as someone in your field, and it makes sense if that's scary.
(Then again, I wouldn't know; I've never really been insecure about my technical skill; I'm more familiar with the fear of people judging the actual content of what I choose to depict, like accusations of being exploitative/insincere/whiny/fetishizing/cringe/pretentious/etc :'D)