I'm a little late to the conversation, but this is actually a topic I feel strongly about. There's a reason why I edited my signature the way that I did in recent months.
Self-deprecation is more often than not just a way for people to preemptively deflect criticism. A lot of people will immediately jump on someone if they start acting arrogant and like they're untouchable, but they'll go easier on someone who immediately admits to their faults and/or seeks out criticism. If they can beat everyone else to the punch, suddenly it's less of a shock when they do say something.
There's nothing wrong with self-awareness or seeking out critique, it's really a good thing, but when it becomes self-flagellation then we have a problem. Self-awareness and self-deprecation might show up together, but they're completely separate things that are also separate in what they mean.
Some people are really terrified as coming off as arrogant and full of themselves, and others are simply just depressed. And as someone who has battled through severe anxiety and depression, many people who are going through that tend to get self absorbed, and I don't mean to put anyone down by saying that. It's just that when you're insecure you're thinking way too much about how other people are going to perceive you and the reality is most people probably give as much of a shit about yourself as much as you do.
And that's the real problem with self-deprecation: insecurity. The solution isn't to be the artist who hates their artwork the most, the solution is to actually build up your confidence and get excited about learning. It's just such a bizarre concept that people think they will somehow get better at handling critique by telling themselves that they are garbage. You can like your work and still want to get better by virtue of the fact that you like art and getting better is fun. It's not always going to be sunshine and rainbows, but I don't think that's the point either.
As far as marketing goes, it's generally a terrible idea to undersell your abilities if you are trying to get your name out there. You are essentially insulting your potential buyers. Why would they ever want to hire someone who doesn't believe in their own abilities? I have legitimately seen people who have said, "I know I suck but..." when it's completely unnecessary. What exactly are you saying to your clients when you talk about yourself like that?
Simply put, self-deprecation in sketchbooks is not funny for the people reading them and they're just kind of awkward and hard to read. It's gonna be transparent as to what you're doing to anyone who isn't on that same mental state as you are too. Just relax and put in the work.