There is an equation that describes this:
#mu = mu^"*" + RTlna#
where #mu# is the "chemical potential" (analogous to but not exactly like energy states) of the solution with the solute in it, #mu^"*"# is the pure solution (no solute), and #a# is a reasonably accurate way of representing the mole fraction of the solvent in the solution. Compounds generally want to achieve a lower chemical potential (or if we are talking about energy, a lower energy state)
The main reason why colligative properties work this way is that if #mu < mu^"*"#, then the chemical potential decreases, causing the freezing point to decrease (and the boiling point to increase).
Basically, on this diagram, shift the liquid line (colored #color(aqua)(aqua)#) downwards.
If you add a solute at all, then #a# can only decrease, because #a <= 1# (because it's a fraction). Therefore, since #lna# where #0 < a < 1# is always negative, the condition #mu < mu^"*"# is always satisfied, and the FP depression and BP elevation occurs.
