I think I have the wrong perspective.
If you take an octave and express it in cents, you get 1200.
Half of that is 600.
A perfect 5th is 1.5 (3/2) of the root.
But 600 is not a perfect fifth, 700 is.
Even more so, if you look at the decimal ratios in this table https://en.wikipedia.org/wiki/Equal_temperament#Comparison_to_just_intonation, you will see that it takes "longer" to get to the 5th, and then from the 5th to the 8th is very "fast".
I have a feeling this has to do with the logarithmic nature of pitch, I feel like I am close to understanding why this is, but wondering if someone can help me out.