Why can't I build an entire jet engine out of carbon fiber?
No, you can not. Carbon fibre composites always contain a matrix component which serves different functionalities, but (in a micro nutshell) bonds and keeps the fibres in place. What you get is a very complex material with lots of lightweight potential, but also very different property profiles compared to metals.

Most matrix materials (thermoset, thermoplastics) will not work up to engine (combustion chamber) temperatures and either degrade/burn or melt/vaporize/burn long before reaching even a meagre few hundred Kelvin (say, 500K). In fact, carbon fibres will not work as well in an oxygenated high-temperature environment, and degrade/burn up as well.

One composite material that works and is used already in engines are ceramic matrix composites, like (amongst others) e.g. C/C-SiC structures, but those are very special animals (and even there the carbon fibre parts are susceptible to burn). Especially in terms of mechanical properties, these cannot compete with superalloys.

But also for many other, ambient temperature parts, metals are much better suited. Think of example of a ball bearing - doing that completely in composite will not work really well (if at all).