I would speculate that reluctance to respond with "I don't know" is imposed onto us through the following cultural factors (I speak based on my experience in the Midwestern USA; perhaps it is different elsewhere):
Teachers Expect Answers
We spend most of our formative years - a decade and a half or so - in a public education setting. In this setting, we are expected to learn and learning is frequently measured by being asked questions and giving answers. If we do not give answers, we do not earn points, we earn a poor grade, and we have failed. It means all of us more or less associate not having an answer to a question with failure.
Failures are Internalized
It's been documented that American culture is distinct from, say, European culture and especially Asian cultures in that personal triumphs and failures are perceived as coming from the individual, rather than from society. When we've been heavily conditioned to perceive not answering a question as a failure, this means we take it personally. If we can't answer something, we personally, are a failure - stupid, ignorant, foolish.
Esteem in the Eyes of Others
To bring this to a conclusion: we're taught that not answering a question means failure, and the failure is personal. If others see us failing to answer, it reflects on us personally and then we become known by others as stupid, ignorant, and foolish too. This can have pretty serious consequences in social interactions. Better to lie, make something up, or appear to know something than be perceived by your peers as an incompetent.