Worf was rescued from the wreckage of the Khitomer colony by a Starfleet petty officer and raised amongst humans in a time when Klingon\Federation relations were somewhat shaky. How did Worf end up behaving with a Klingon cultural identity? How did the Klingon concepts of honor and behavior get so firmly enmeshed into his personality?
I suggest that Worf doesn't act very Klingon at all. He is instead probably acting out a warped sense of what he remembers Klingons being like, from when he was young, combined with the tilted educational materials avaiable about Klingons while growing up with the Rozhenkos. Together they would go a long way to explaining why Worf isn't very Klingon at all. While it is true that Worf holds honor in very high regard, and enjoys fighting as much as the next Klingon, he doesn't really know how to behave like a Klingon. When he is with other Klingons he rarely really fits in: when they're drunk, he's sober; when they are laughing he is serious.
I believe the conversation between Guinan and Worf sums it up nicely in TNG Redemption Part 1:
GUINAN: You know, I had a bet with the Captain that I could make you laugh before you became Lieutenant Commander.
WORF: Not a good bet today.
GUINAN: I've seen you laugh. I like it.
WORF: Klingons do not laugh.
GUINAN: Oh yes they do. Absolutely they do. You don't. But I've heard some Klingon belly laughs that would curl your hair.
GUINAN: Your son laughs. He's a Klingon.
WORF: He is a child and part human.
GUINAN: That's right. And you're not, you're full Klingon except you don't laugh.
WORF: I do not laugh because I do not feel like laughing.
GUINAN: Other Klingons feel like laughing. What does that say about you?
WORF: Perhaps it says that I do not feel like other Klingons.
GUINAN: [...] So how is he? Your son.
WORF: He is having difficulty adjusting to life on Earth.
GUINAN: I can see where it might be hard for the little guy. Living with humans, being Klingon. Could be very confusing.
WORF: It will not be easy for him.
GUINAN: No, it won't. But at some point he's going to want to know what it's like to really be a Klingon. Just as you're learning.
During the conversation Worf himself says that he doesn't feel like other Klingons. And a little later Guinan points out that Worf is only just learning what it really means to be Klingon. You can see that later, especially in Deep Space Nine, Worf does behave a bit more like a Klingon.
Five is a considerable number of years to be in a culture - living even one year in another country can profoundly affect a person, and those five years that Worf lived in Klingon culture were the first five years of his life - highly formative years (assuming Klingon maturation is at all like human maturation)
Not to mention, he grew much more during those years than you might realize. As per this answer to a question about Klingon Age:
However, their maturation also happens at different rates than humans. In DS9 6x03, Sons and Daughters, Worf's son returns, appearing older than he should:
Many fans felt that Alexander was far older in this episode than he should have been given his age as established in The Next Generation. Bradley Thompson countered this argument by pointing out that it has never been established how fast Klingon children grow.
Alexander was born in 2366 and that episode takes place in 2374, making him about 8 years old and already a member of the Klingon Defence Force.
Emphasis mine. In short, a huge amount of his maturation took place in Klingon Culture during those 5 years.
And, as Xantec points out, he really only upholds the general culture of Klingons, but has trouble fitting in among other Klingon Adults, who have had a chance to learn the nuances of Adult Klingon social interaction.
Worf is a different species from humans, with entirely different hormones, neurology, etc. Much of any species' behaviour is biologically determined, not cultural. Your question is like asking why a dog raised by humans "acts so dog".
In one of the episodes of TNG its explained that Worf was told about the Klingons and their behaviour by his parent (I think it was his fostermother). It may have influenced him enough, in addition to his genetical background?
In the episode "Let He Who Is Without Sin...", Episode 07, Season 05 of Star Trek: Deep Space Nine, Worf explains to Jadzia Dax his behavioral attitude, when she asks him why he is so different from all the other Klingons she and her previous host Curzon have known.
He tells her that growing up on Earth as a child, he was very much like other Klingons, especially Klingon children. But one day, when he was thirteen years old, he was in a soccer match, and during the winning goal, Worf headbutted an opposing player, to make the shot. The human boy Worf had hit with his Cranial Ridges died of a broken neck.
It was then that Worf realised that compared to Klingons, other races, especially Humans, are very fragile, and if he wasn't careful, even a simple Klingon act of joy and celebration, could harm someone. It was this moment that made Worf stern and cold, especially compared to other Klingons. Worf loves his people and their ways, but he realises that Klingons can be careless in their actions, when compared to other races.