Worf wasn't raised by other Klingons though. When he was very young his dad died in a space battle with the Federation, and he ended up being adopted by a Russian couple on earth.
They genuinely loved him, and wanted what was best for their son. As part of this, they didn't want him to grow up alienated from his cultural identity as a Klingon, and made a point of exposing him to Klingon cultural traditions as a major part of his upbringing.
When Worf interacts with other Klingons on the show, there's a distinct cultural divide.
He's been raised with heavy emphasis on Klingon values such as aggression and honor, but only as seen through the filter of Federation (i.e. 1990s american liberal) values.
As practiced by native Kilingons, Klingon cultural values are expressed very differently than how Worf understands them. This frequently catches him by surprise and makes him feel like an outside.
@shoofle It's real good. Worf is general is consistently one of the most interesting characters :)
Now here's the interesting part, which was implicit but not overt in the show.
Worf's parents were raising him basically on the Wikipedia version of Klingon culture. They did their very best to expose him to Klingon rituals and cultural values, but only with the imperfect knowledge of cultural outsiders. There was no Klingon community on earth they could participate in. They could teach the declarative content and nominal meaning of the culture, but none of the actual texture as practiced.