Half a course is NOT better than nothing - it basically kills off only the weaker bacteria, leaving behind only those that have started mutating a resistance to the antibiotic.

An effective course of antibiotics leaves no possibility for survivors.

Here’s a good demo of what happens when you give them a graduated path to climb (such as by taking half a course of antibiotics: https://www.youtube.com/watch?v=plVk4NVIUh8