The reason is fairly technical, but has to do with commonly accepted rules of heraldry, specifically what's called the rule of tincture. In European heraldry, either two metals or two colors aren't allowed to be placed directly atop or against one another; they're separated by a white band, called a "fimbriation," to allow the colors to stand out more from one another. (Note that you can find loads of exceptions to this rule, but that it's the starting point for this answer.) You can see this fimbriation on the union flag used 1707-1801 -- it's the white band around the St. George's cross.

The Irish cross (the red cross of St. Patrick) is also countercharged with the white cross of St. Andrew from the Scottish flag -- that is, each of them is given half of the space when they're overlaid with one another, so that the white cross and red cross follow one another around the flag clockwise.

The white fimbriation makes the St. Andrew's cross appear wider, and it does also mean that there's a "right side up" to the flag. Apologies for the Wiki link, but you can see here from this diagram how the two crosses follow one another in position clockwise.