Why do colligative properties only depend upon the number of particles in solution and not what ...

The colligative properties are:

Vapor Pressure Depression
Freezing Point Depression
Boiling Point Elevation
Osmotic Pressure Elevation

These properties depend on two things, really:  the number of properties in solution, and the nature of the solvent.  Different solvents have different cryoscopic and ebullioscopic constants which help to explain how they behave when we dissolve things in them.

The easiest example to look at is an ionic compound dissolved in water.  Water forms what's known as hydration shells around dissolved particles.  Water is a polar molecule, with a partially positive end and a partially negative end.  Each particle of solute is surrounded by molecules of water; the partially positive side of the water is attracted  to negative ions (anions), and the partially negative side is attracted to positive ions (cations).  The resulting complex is heavier and larger than a single molecule of water; therefore, it is more difficult to break it up and force the water to boil. Their size also makes it harder for these hydration shell units to line up into a solid mass, meaning they have to be even colder in order to freeze.

Your right - colligative properties seem to depend only on the concentration of solute particles, not on the nature of those particles. It used to bother me too. You'd be forgiven for thinking that charge or size might have an impact; but they don't.
In the case of boiling - in adding a nonvolatile solute to a liquid, the surface area for the escaping solvent molecules is reduced. That's because some of that area is now occupied by solute particles. Therefore, the solvent molecules will have a lower probability to escape the solution than the pure solvent. Hence the temperature for escape needs to go up.
In the case of freezing - the solute's presence interferes with the rate at which solvent particles can transfer to the crystals of the precipitating solid.
The answer is almost a statistical argument.