what is the exact reason why belt drive systems are not available on carbon frames?
In addition to the other answers that point out that there is no such reason, because the premise itself is false, I'll point out that while a split frame is a common way to accommodate a belt drive, it's by no means the only.
The other main approach for accommodating belt drive is to use an elevated chain stay, which allows the drive belt to pass entirely under the chain stay, rather than having to be routed through the triangle of the rear frame. This avoids having to split the frame at all. This is the approach taken by Olsen, mentioned in a different answer, as well as several other bike manufacturers who support belt drive configurations.
Reasons for lack of availability, to the extent that there even is less availability for carbon frames as compared to frames made of metal or other materials, are much more likely to relate to market conditions, i.e. that there's rather much less demand for belt drive in that market due to differences in the way the bike is expected to be used.
Belt drive trains are typically heavier than an equivalent chain drive train, and very often are chosen for riding in conditions where the use of the belt significantly reduces maintenance hassles (e.g. due to rainy or muddy conditions, such as for commuting or off-road). Both of these factors have a small (but certainly non-zero) intersection with the goals of riders who choose a carbon fiber frame.
There is no technical reason that a carbon frame couldn't be designed to accommodate a belt drive system, and indeed there are examples of both major design approaches in the carbon fiber frame market.