Several commenters here mention math formulas (and I'm guessing other math constructs) as a reason to use (La)TeX. I'm not a mathematician, so that reason doesn't work for me. But there's another reason for me, which is analogous. I'm a linguist, and linguists often use an aligned interlinear style in which each word in some sentence of a foreign language is glossed underneath with its meaning (and often morphological breakdown into stem and affixes); the foreign words and their glosses are supposed to line up vertically (so there may be extra spacing between words, typically but not always in the foreign language line). If the paired words+glosses of a sentence don't fit on a pair of lines, the lines hold as many as possible, and the pairs are continued below.

This is extremely painful--nearly impossible--to do in Word. There are LaTeX macro packages that do it quite well.

(When the foreign language is broken down into morphemes in its script and there is a gloss line, you end up with a triple of aligned lines, instead of just a pair. And when the foreign language is written right-to-left, other issues come up. But they can be addressed in the LaTeX macro packages.)