Suppose you need to convert a list of time, which is the time when a file is created. It is in 12 hour format and you need to convert to 24 hour format. That looks like something that can be asked of you by your project manager in your actual projects. Now replace the 12 hour format time object with a square looking time object and the 24 hour format with a triangle looking time object. The example is to describe Functional Programming approach to do this problem. The example’s job was not to explain the need for functional approach but rather to show how we would tackle the problem if we use Functional Approach.
As for the convincing part, have you ever seen callback hell in your project? That alone is a hassle enough (at least was for me) to convince me to use RxJava. You could have a look at this if you need more convincing: