Answer
The number of degrees of freedom increases when the samples are larger. As the sample size increases, it becomes harder to obtain a sample whose mean is far from the population mean. So the spread decreases.
Work Step by Step
Suppose you obtain a sample of 5 people and you ask then their age. It is not so difficult to obtain 5 young people whose mean is significantly bellow the population mean age. But, if you obtain a 100 people sample, it is almost impossible that all of them are as young as the 5 above.
