I don't entirely understand the why, but here is what I do know. The main reason for this convention is that F2-F1 gives a plot where the X axis better matches tongue position in back round vowels. The problem with bare F2 is that it makes vowels positions slope to the right as you go up (with [u o ɔ] not matching [ɯ ɤ ʌ]), but F2-F1 makes the back round vowels track actual tongue position, so that they slope to the left. The exact reason for this is somewhat mysterious to me.
Part of the mysterious nature of the relationship between formants, tongue position and vowel charts comes from the traditional habit of thinking of vowel articulations as being a governed by two independent factors. However, a lifetime of work by Fant and others has demonstrated that a better model is a tube with a constriction, so there is as a first approximation only one factor (the second approximation adds differences in tube length, as a function of lip protrusion).
Rounding lengthens the tube, which lowers all formants. The effect of rounding is greatest on F2, and it is greatest in back vowels. This bit of subtractive magic has the effect of "figuring out" what the lowering contribution of rounding is, and mostly removing it from the vowel plot. What is left, then, is an X value more based on tongue position, rather than the total length of the front tube.