Interesting. Many cultures are phobic of self-deprecation, particularly those that will brook no threat to the hierarchy. People who can laugh at their own absurdity can usually spot the absurdity in others. People who think they're better than everyone else usually don't want to hear otherwise.
Self-deprecation is the hallmark of egalitarianism, which was a big part of Australian culture, although less so now. It's a way of helping people feel included.
For example, I was once introduced to a chap called Barry*, "This is Barry, one of the best guitarists and singers in Tasmania"
Barry was clearly nervous, so I quipped "Hi, I'm Rob, I'm the worst guitarist and singer in Tasmania."
We all laughed and it broke the ice. It facilitates a collaborative mindset rather than a winner-takes-all mindset. The damage usually comes from people who don't get the joke, and perhaps might even use it against you. If this is your personal experience, I can understand why people might avoid it.
As you've said, their is much value in collaboration and being open to the participation of others is a good thing.