Why do parents reward their children with unhealthy food and drinks?

No food is unhealthy. It's all about amounts. Eating or drinking too much of any substance, including water, is bad for your health. The things we call "unhealthy" are those things where it is easy to eat too much. That happens for a reason, typically because these are things which we're genetically disposed to ENJOY eating. This answers your question then. Most unhealthy foods would be perfectly healthy -- if not for the fact that human beings tend to like them so well that they overeat them.

They do it because it's easy and cheap. A lot of parents are just trying to do whatever it takes to shut their kid(s) up and they don't care whether the means are unhealthy or not.

...Because they are not willing to tolerate the uncomfortable, and sometimes exhausting, experience of patiently and creatively engaging with their children in the spirit of real teaching and guidance...that takes remarkable amounts of energy and commitment.  It's easier to train kids to respond to addictive drugs like refined sugar...

The   very important reasons why parents buy these unhealthy and junk foods are   because it is easily available and carrying to different places are not much   difficult. Also, today these unhealthy foods are available for fewer amounts   when compared with the healthy foods. So, on the whole easiness and change of   life style all made junk food to be the most preferable food when compared   with the healthy foods.

A child’s taste can be influenced in social situations, for example by displaying and promoting disgust towards a certain food. Food refusal is reinforced throughout a person’s development, feelings associated with food or experienced while eating food can promote fear in trying something new.