This is probably going to be something specific to your environment, so not really possible to give a real answer.
The most likely explanation is that your server doesn’t actually have the mcrypt extension installed. You could try to verify that, and install it if need be.
However, a better idea could be to update Craft to the latest 2.x version (2.9.2). Craft has actually bundled an mcrypt shim since 2.7.0, so it can run without that extension altogether. Fortunately, the Craft 2 releases since 2.6 don’t really have any big breaking changes, so updating shouldn’t be a major pain. And, with the latest Craft 2 release you should be able to bump PHP up to 7.4 if you want to (assuming all your plugins are updated and supports that version as well) - which could be a good idea from a security standpoint.