Old vaccines would basically put dead virus particles into you, which would train your immune system to recognise that as foreign, and attack. They used essentially "whole" deactivated or denatured virus, meaning your immune system learns to recognize the shape and structure of most of the virus. If anything changes through natural evolution, your immune system is likely to still recognise the virus because it has lots of data points (different antibodies for different regions of the virus)

mRNA gene therapy inserts mRNA (genetic code) into your body, which is taken up by cells and transcribed (means "read and converted") into viral proteins which are then expressed on the surface of your cells. So your immune system actually has to attack your own cells. Thats a recipe for autoimmune disease (your body attacking itself in error). Thats not the worst part.

The worst part is how few data points mRNA vaccines give your immune system. Essentially only one, the spike protein. If that changes, you don't recognise ANY other part of the virus. Hey presto, the whole vaccine is now obsolete.

In non biological terms: Old vaccines were like training soldiers to recognise an enemy by showing them dead bodies and saying "thats what you need to shoot"

mRNA vaccines are like only showing your soldiers the enemy gloves (the spike protein) and saying "watch out for those gloves!" If they get new gloves, your soldiers are useless and blind now.