When I was very young, I remember being taught the lesson that I should make fun of myself before other people can do it because I've already acknowledged whatever they were going to make fun of, thus taking the wind out of their sails. I tried it out because nothing else I'd tried to stop people from bullying me was working, and it must have had enough success (though not 100%) to keep doing.
For most of my years in college, I tried to be many people's friend. And I wanted to understand how people work, why they thought the way they did, and why they chose the actions they did. This allowed me to get very close with people and build some strong connections. It also allowed me to reach out and try to help people when they were in pain.
One phenomenon which I encountered a great deal was people telling me that they were terrible people. It was incredibly confusing to me because the people who were saying it were people I liked. They were people I had respect for and enjoyed being around. At the time, the only thing I could think to tell them was that they were wrong; they were perfectly fine people.
What made this phenomenon extra shocking was that people strongly argued with me that they were terrible. They had many reasons, cited examples, even claimed to have witnesses. They put forth tremendous amounts of energy to assure me that they sucked.
The most surprising part, though, was that they convinced me. For one reason or another, even if it was simply attrition, they turned me around and got me to agree that they were awful.
Over time, I phased out contact with them. I gave them less of my energy and time and interest until at last they were gone. It wasn't a vindictive thing per se. It's just that I didn't want to be friends with terrible people.
Suddenly, the advice I got all those years ago was wrong. Self-deprecation is dangerous. It may stave off bullies, but it may just backfire and turn people away.
The true lesson here is that you are what you believe you are.
If you believe you aren't "a writer", then you aren't. If you think you're a bad writer, then you will end up either being boring or annoying. But if you believe that you are doing better and that it's a good endeavor to pursue, then you will be always improving and happy for it.
Not just you, but everyone will believe what you believe. This is good since, as a writer, your job is to convince people that what you are saying is real and valuable. However, this sword cuts both ways. Keep telling yourself that you suck, and people will believe that, too.