That's, uh, a pretty intense reaction to some curves.
There is a long history of rounded corners in graphic design. In the real world, perfectly sharp edges do not exist. Even on the printed page, ink bleed tends to gently round all corners.
This is a good thing, because sharp corners interact poorly with some parts of our visual system. Sharp corners in a design can be as jarring as extremely high contrast or saturated colors, which are also best avoided in designs where the intent is to let the viewer focus on the content and not the form.
A slight amount of corner rounding in digital graphic design can lead to a look that is easier on the eyes, less distracting, and more approachable. (The design here uses more rounding than necessary, but I think it's driven largely by fashion and the above principles and not some dystopian desire to infantilize you.)
See:
https://en.wikipedia.org/wiki/Grid_illusion
https://en.wikipedia.org/wiki/Lateral_inhibition
https://en.wikipedia.org/wiki/Pattern_glare
http://people.sunyit.edu/~lepres/thesis/principles/63_pdfsam...
http://macknik.neuralcorrelate.com/pdf/articles/troncoso_et_...