I'm assuming this is the mini-SD card inserted into the slot on the side of a Mavic Pro, or
Mavic Pro 2 ... yes??
For such a small card, the mini-SD card has a proportionally large cam on the side of it that acts as a 'mechanical' latch to keep the card in the slot and engaged. As you rightly point out, the construction of the cam structure on the side of the card, also engages the release mechanism when the card is pushed in further than the latch position. In other words, if you can't make the card pop out by pressing it in a little further with the blade of a screw-driver, then yes - there is something seriously wrong in there ...
I'm assuming that you know the card has been put in the right way round - yes? It is difficult to put the card in upside down - with the latch cam on the wrong side - but not impossible if it's forced! If that's been done, then the card slot is going to be pretty much u/s! If the card has been inserted the right way round, and the card still won't come out, then that also means the card slot mechanism is probably u/s. The slot/latch mechanism is designed to be lightweight and simple - so - if it goes wrong, it tends to stay wrong - and even if it did free up and let you have your card back, it's highly likely that it would do the same again soon.
Here's an article about this type of card interface ...
https://www.quora.com/How-is-a-memory-card-held-in-mobile-phones-How-does-the-mechanism-work
That may be helpful, but unfortunately, I think you'll need to look at a way of either getting the mechanism replaced on the card that its a part of, or get a new card. Either way - you'll be hard pressed to get the micro-SD card back without at least pulling things apart to get down to board level.
Maybe
@Thunderdrones can give us some more advice about how to fix this problem ...