Why are most cirrus clouds present over the equator and over tropical continents?
Clouds require moisture and therefore high clouds will exist in regions with upper-level moisture.  Synoptic scale ascent is on the order of cm/s and this is not an efficient way to bring moisture from the surface to the upper levels.  

Consider this water vapor imagery:
 
Source: College of Dupage NEXLAB

In this image, the color represents the humidity of the mid and upper levels of the troposphere.  Brighter colors represent moisture at higher levels.  Darker colors represent moisture at mid levels.  Black represents dry mid and upper levels.  

The brightest whites (highest level moisture) at this time are along the ITCZ and associated a mid-latitude cyclone in the northeastern US.  These are areas associated with convection, which unlike the synoptic scale flows is an efficient transport of moisture into the upper troposphere.  This convective outflow will first be associated with the "anvil" top of the thunderstorm, but as it is advected at the upper levels can manifest as cirrus clouds.  The ITCZ is driven by equatorial convergence and the upward branch of the Hadley cells.
Mid-latitude cyclones have a so-called "wet conveyor belt" that transports near-surface moisture into the mid and upper levels which can then manifest as upper level clouds (or lots of rain/snow). 

To answer "why are most cirrus clouds in the tropics?" I would associate that with the large transport of water vapor into the upper levels by the persistent convection in the ITCZ.