I was wondering that too! I got to the end and still no explanation of 210×297mm.
Well, it turns out that it's based on the fact that A0 is defined as having an area of ~1m², then each subsequent size halves the area. So A4 has dimensions that give an aspect ratio √2 and an area of ~1/16m².
A0: 1,189 mm × 841 mm = 999,949mm² ≈ 1m²
...
A4: 297 mm × 210 mm = 62,370mm² ≈ 1/16m²
"The A0 base size is defined as having an area of 1 m² ... rounded to the nearest millimetre, 1,189 mm × 841 mm".