Most functions are not linear. This may seem too obvious to be worth mentioning, but it's very easy to assume that various functions that appear in real life are linear, e.g. to assume that if a little of something is good, then more of it is better, or if a little of something is bad, then more of it is even worse (apparently some people use the term "linear fallacy" for something like this assumption), or conversely in either case.

Nonlinearity is responsible for local optima that aren't global optima, which makes optimization a difficult task in general: it's not enough just to look at the direction in which you can improve the most by changing things a little (gradient ascent), but sometimes you might need to traverse an uncanny valley and change things a lot to get to a better local optimum, e.g. if you're at a point in your life where you've made all of the small improvements you can, you may need to do something drastic like quit your job and find a better one, which will temporarily make your life worse, in order to eventually make your life even better.

The reason variance in financial investments matters, even if you only care about expected utility, is that utility isn't a linear function of money. Your improvement in the ability to do something is usually not linear in the amount of time you put into practicing it (at some point you'll hit diminishing marginal returns). And so forth.