The phrase comes from a poem by Alexander Pope (May 21, 1688 - May 30, 1744) called 'An Essay on Criticism':
A little Learning is a dang'rous Thing;
Drink deep, or taste not the Pierian Spring:
There shallow Draughts intoxicate the Brain,
And drinking largely sobers us again.
The phrase is usually interpreted to mean that it's better to learn something properly than learn just a little about the subject.
Many of us, while studying a subject, reach a point where we believe we've learned the lot, that we know it all. From here we frequently look upon much older or very highly-experienced people in the particular field and decide we know better.
This is where we can easily make mistakes!
In some areas these mistakes can be highly dangerous, to ourselves as well as to others. We must take care to retain humility, without too much insecurity. When we begin to think we are capable of doing what others have studied for years to learn to do, this is when we must stop and examine our skills and our limitations, and especially this is when we should seek advice from those who've been learning the subject years longer than us.
This is not to say a lot of learning necessarily makes any person infallible, but it usually takes a lot of learning to be able to see that.
For exapmple: Alexander Pope's words are sometimes misquoted as, 'A little knowledge is a dangerous thing,' which just goes to show a little learning about English literature and the idioms of English necessarily give us the knowledge to always get it right!
A sadly fairly common example of the danger of taking a little learning to mean we know a great deal more than we do is the person, maybe a paramedic or nurse, or simply someone who's read a great deal about the practise of medicine, who fraudulently sets themself up as a doctor and goes on to prescribe courses of treatment and even perform surgical procedures until they're almost always caught.
We hear of these cases from time to time, and of the tragic damage which can be caused to trusting victims.
While there's a pathological basis to the motivation behind the actions of such frauds, the whole thing frequently begins with that 'little learning', followed by jealousy of those who've qualified in the field and by feelings that if these qualified people can do it, so can I.
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This phrase refers to the idea that having limited knowledge on a topic can be risky, as it may give someone a false sense of confidence or understanding. It suggests that partial understanding can lead to making poor decisions or judgments due to overestimating one's expertise. It emphasizes the importance of thorough and comprehensive learning.