Here is what I've seen (and been guilty of):
Two pieces of code in different parts of the codebase are very similar. They have nothing to do with each other - even semantically. But the code is very similar. So someone thinks this is code duplication and creates a function/class/whatever that both pieces of code can use. Repeat all over the place.
Then one day, one of those two places needs custom behavior. I can either change that function/class and create complexity (have to now support two use cases). Or I can stop using that function/class in that place and go back to the old solution. Sometimes, this is quite a lot of work as aggressive "DRY" leads to a fair amount of coupling - there could be a few layers of DRY'd code there to untangle.
I put "DRY" in quotes because none of this really is DRY. DRY originally was about requirements - not code. No requirement should show up in multiple places in the code base. In this example, even though the code was almost identical in both places, there was little else common. They dealt with different requirements, for completely different reasons. They should never have been refactored to use a common function/class.
These days people keep talking about over-use of DRY, but they're really complaining about overabstraction of disparate code - not the DRY in the requirements sense.