The famous proverb: "Everything you say should be true, but not everything true should be said." helps to distinguish the difference between honesty and openness. The first part basically means: "Be honest." and the second part: "Don't be open." Even though this proverb has a nice ring to it, a lack of openness can just be as harmful as not being honest.
A lack of honesty is frowned upon in our society. People that lie and cheat quickly gain a bad reputation. So it comes naturally to refrain from this behavior.
A lack of openness will often come with more subtle drawbacks. If your manager asks you how your project is going, and you don't tell him about all the problems you ran into, because you are scared how he will react, this will lead to a bad outcome later. You will have much more stress because not only do you have to fix all these problems, you always spend energy on hiding them. And the manager will learn to distrust you.
In a relationship, if you just always swallow the problems and don't voice your concerns, it will just grow.