Why developers are so paranoid about failing Integration tests and Why this is not a problem

When it comes to developers talking about Web Integration tests - you may hear something like "Test should not fail if I move this button" or "If the text on the button changes slightly - test should still pass"

But from my point of view it's ok to fail test because of that. And I would even believe failing test more than passing one.

For a long time I cannot understand the reason of this misunderstanding. And today while reading a book on unit testing - I finally got it.

tl;dr changes in Web Page are more sensitive than changes in API