When I try to launch older versions of Minecraft using the new launcher. It tries to load and then nothing. I get no error message or any error to speak of. It tries to start and immediately quits. I even checked the Linux terminal using the top command to check if if was running in the background. It showed absolutely no Java processes running.
What version of Java do you use to start Minecraft? Versions prior to Minecraft 1.13 are unable to be started with Java 9 or newer, so you need to make sure that Java 8 is installed. On Linux, you unfortunately need to do that yourself.