The more people know you own Bitcoin the bigger the possibility that someone might try steal it from you.
This is something that I often think about. On one hand, obviously keeping your involvement with bitcoin private is good for you own personal security, but on the other hand, I want to be able to spend bitcoin in person, and I not infrequently talk to local merchants, vendors, tradesmen, etc., about accepting bitcoin (with some success, but that's another story). If no one ever told anyone else that they want to spend/use bitcoin, then there would be no adoption and consequently the price would stagnant and fall.
I don't think simply owning bitcoin makes you a particularly attractive target for scammers, hackers, or thieves. They need to know you are holding enough bitcoin to make it both worth their time and worth the risk. If you have a number of different unconnected wallets, with your main holdings separated, well hidden and not publicized, I think you are relatively safe.
The set up Nunuface is describing is good from this point of view, I think. If his wallet was to be hacked or he was subjected to a $5 wrench attack, he could give away the holdings in his main wallet without it being too big a deal, knowing that his main holdings are safe behind a passphrase.