It’s because for every pair of irrational numbers, there is a first place in their decimal representation where their digits differ, which means you can construct a number with finite decimal representation that fits between the two, which thus is rational.

In other words, it’s because while there are uncountably many irrational numbers, their representation is still only countably infinite each.

Or in yet other words, uncountable infinity is only a teensy bit larger than countable infinity, not that much larger. Consider that every prefix of an irrational number is a rational number. ;)