Why a highly precise measurement does not always mean a highly accurate one?

Think of it this way. I have a bathroom scale. I step on the scale in the morning five times and it reads 150.1, 150.2, 150.2, 150.3, 150.1. The average weight is 150.18. The measurement is precise to within a few tenths of a pound. Nevertheless, it is not accurate. However, when I go to the doctor's office, he says I weigh 160 lbs. His scale (or balance, if you wish) is certified accurate. My bathroom scale is apparently not accurate.

In this case, there is a systematic error -- probably caused by a calibration error. There is also random error (that's why each reading isn't exactly 150.18).

Random errors usually predict precision, systematic errors (or minimizing them) are responsible for accuracy.

Quite simply because the definition of the word "precise" is not the same as the definition of the word "accurate"They are two completely different things and hence you can be precisely accurate or precisely inaccurate depending on your ability.