The most obvious reason why CLI is important is because it is a pre-requisite for future concepts taught in Universities and for work. CLI itself is a very powerful tool as it gives you access to the file system and perform a variety of useful tasks.
From the top of my head, one key feature of CLI is that you can perform SSH in order to send, copy, and explore files from a remote to local. You can also check system log files for issues and configurations. This is different than sharing screens and remote connect because we are talking about access to file systems and opening a pipe to your own computer for filestreams.
Extending further, CLI is the basis of multiple mainstream applications such as Git, Node, and NPM. As developers, we move away from running executable to setup our development environment and applications, therefore it is imperative what we know and understand CLI. For example, setting up AngularJS or React (two of the hottest front-end technologies) is as simple as npm install ... as posed to unzipping from Git and running a whole bunch of scripts. Now moving on to Git, any seasoned developer will tell you that nothing is better than CLI for Git. Sure there are a lot of UI'sUIs for Git, but they are not as feature rich as the CLI and often times buggy. You can't get away with being a developer and not use some form of source control, so it is good to get familiar with CLI early in your life.
Lastly, the biggest non-reason would be how cool you look infrontin-front of non-programmers programming in that black and white terminal ;)