Just WHY are driving examiners striking?

The reasons are in the article alongside.

In short, DVSA has been required by government to reduce the longer-than-desired waiting time for a driving test.  (As with many national services, such as the NHS, this arose due to Covid).

Government hasn't allocated more money to achieve this so managers have taken various steps to improve the quality of teaching (by self-employed instructors, over whom they ultimately have no control) get more productivity from existing staff (over whom they do).

Not all these steps are liked!  Some staff who'd been promoted but still hold the "warrant" to assess learners, have been asked to return to it.  Newcomers aren't being offered long contracts.  Etc.