I really don't know why one person should create cavalier and the other one should create cabinet when it comes to oblique projection, are there any reasons why one should use cavalier instead of cabinet and vice versa?
As Karlo's comment pointed, every 2D representation of a 3D object has some loss of information. Furthermore, drawing that representation and recovering information from it (taking measures) has some level of complexity. Choosing among available representations is a trade-off between different losses of information and levels of complexity. A few pros and cons of each may be:
Cavalier: - A bit easier to draw and measure in the z axis. - Less natural perception of volume (objects seem enlarged along the z axis). - Better perception of plan.
Cabinet: - A bit harder to draw and measure in the z axis. - More natural perception of volume. - Plans more stretched compared with plan views.
Therefore, cavalier is likely to fit better things like drawing fortifications and cities, where plan matters the most, where cabinet is likely to be better drawings of vertical furniture (wardrobes, for example) where the elevation is more important.
In addition, if oblique projections are seen as a simple way to simulate a perspective, they simulate perspectives with different points or view (lower for cabinet, higher for cavalier). Cabinet is likely to be a better fit for objects best seen from the ground (like furniture) while cavalier is likely to be a better fit for objects best seen from air (like cities).