In hindsight, I think they were completely right and I feel kind of lucky that they drilled that in so much, because even into my mid 30's I don't have a ton of trouble or resistance to picking up new things. Sometimes I don't love the way new tech is going [1], but I still try my best to keep up with what's in demand in the industry (generally looking at job boards and looking at their keywords and making sure I have at least a cursory understanding of the stuff they're talking about). I will admit I don't completely love that AI is being used instead of junior engineers in some cases, largely because a lot of AI code is shit or flatout wrong in non-obvious ways, but I still have tried my best to utilize it and learn from it because it's clearly the way that things are going. [2]
I've been hired and lost/quit more desk jobs than anyone I know, and I attribute my ability to find work quickly to this characteristic.
[1] e.g. treating memory like it's infinite, disregarding CPU performance as a means of "getting more shit done", making configurations (arguably) needlessly complicated like Kubernetes, etc.
[2] For example, my latest project has been building an HLS and Icecast "infinite radio station" which picks a random song from my collection, feeds a prompt to OpenAI for DJ chatter in between songs,