Is there an intuitive way to think about implicit differentiation?

Take Real Analysis.

Sorry if that's bad advice, but it's what I had to do

So, around the points where the derivative you obtain is not defined, it means that Y does not change according to changes in X, which means you cannot write Y as a function of X because oh that point I does not depend on x (when, for example on the circle, Y is 0 and the value of X depends on the radius, So x can be whatever -the value of the radius - and Y will be 0, thus not being a function of X).

In real life, think it like... correlations... Like, you not having money is due to a drinking problem and having lots of friends, one could say and modelate it assuming you drink too much because you have lots of friends (Y is a function of X), but that is not true if none of your friends drink or all your drinking friends die of liver failure (y cannot be expressed as a function of X in these cases). It's the best example I can think of, applications in real life do apply the existence of correlations (it is implicit in the fact that Y can be written as a function of X, they must be correlated somehow), but I can't think of something you can go an read to understand it. Also, excuse my poor English, I literally learned this shit this year so I must not have the best grammar. I hope I could convey something in my post.