Nonetheless, I maintain that modern usage puts words with a di- prefix into a category that generally means "separate" or "separated in two".
That's because you are confusing words with the prefix of
di- (meaning
two) and the prefix of
dis- (meaning
apart). The comparison in question is between the prefix
di- and
bi- so you need to be sure you are comparing apples with apples, and not with bananas.
Whereas, in modern usage bi- words are in a category meaning "two of". Hence, angle bisection means there are two (equal) angles. The word dissect means to cut from or out of.
Because dissect comes from the Latin
dis- (apart) and
secare (to cut). And not
di- (two).
And if we have two genders, why aren't we bimorphic in that context? Why are we sexually dimorphic (i.e. gender-separated).
If we were sexually bimorphic, we would be both male and female, ne c'est pas? Or, someone born with both genders would be (this happens occasionally).
The reason is simple:
morphe is a Greek word meaning form or shape. Hence it will take the Greek prefix rather than the Latin - hence dimorph rather than bimorph.
Your theory is simply wrong, I'm afraid. Hopefully the above explains.
If in doubt, list all words that you think have the root
di- and
bi- and we should see that both roots mean the same thing: "two", "twice", "double" etc, and that the one we use depends on the origin of the root word.
And even then you have to be aware that Latin words may have originally stemmed from the Greek.
E.g. Dipole - which seems to come from
di- and
polus, so a Greek prefix and Latin root, but the Latin actually comes from
polos, the Greek.
If there is any trend it is that scientific words tend to use the Greek (because they take their technical words primarily from Greek rather than Latin, although medicine uses Latin rather than Greek) hence physics and chemistry would use dipolar, medicine would use bipolar (noting that the root word can be either Latin or Greek, hence there is still consistency with
di- for Greek,
bi- for Latin), dioxide rather than bioxide etc.
But do not confuse the Greek
di- with the Latin
dis- as they mean different things, and this might well be where your theory arises from.