The problem is when things change. A simple example - you build a classification of all life and it is built upon the idea that everything "is a" plant or animal. And then one day it turns out there are fungi. This is not a fun situation to deal with and inheritance makes it a lot harder because the "is a" relationship is driving a ton of your logic.
IDK I don't want to get to into it beyond that, many people have written quite a lot on the topic.