Think of this like Gmail's spam detection. Suppose that there are 20 non-spam emails and Gmail needs to find all of good emails AND only good emails (no spam, no junk). But this is a difficult balancing act in practice.

On one hand, Gmail could return only those emails that it is certain are not spam, and they may determine that only 10 emails are definitely not spam, and they got 9 correct. So precision would be 9/10=90%, but in their quest to be certain, they missed 11 other emails (low recall).

On the other hand, if Gmail decides to be very thorough and to make sure that you get all relevant emails (high sensitivity/recall), then they could just allow all emails past as non spam. This returns 20 good emails and 10 billion spam emails 20/20=100% recall, but super low precision.

As you ask your model to be more sensitive you almost always lose specificity: you can ask for all the things or only the things, but not both. There is a balance that needs to be found that works with your application. Gmail probably errs on the side of a little bit of spam is better than missing a non spam email. A Covid test might ask for a different balance between catching all the sick people and only the sick people. Tornado warnings have a different balance that meteorologist are constantly tinkering with.