I don't want to dig out the math figures, because god knows they're hard enough to scribble freehand, but as you add more samples, the difference between your null hypothesis and sample average shrinks in regards to what establishes a p<0.05. Let's just use not-real numbers: if a sample of 100 people has a difference of 5 units from the null hypothesis, and has a p value of 0.1, a sample of 10,000 with a difference of .1 unit might have a p value of 0.02. In the quote (that I can't seem to find now), the essential wisdom to take is that if you dragged in enough samples, you could find a statistically significant difference because your null hypothesis would never be exact, so even the smallest of differences would generate a low p-value. It's why whenever you see a p-value, you should definitely see an effect size estimate nearby, such as cohen's D.

Here's a paper outlining some of this in much better words than I have.