Why do Decision Tree Learning Algorithm preferably outputs the smallest Decision Tree? I have been following the ML course by Tom Mitchel. 
The inherent assumption while using Decision Tree Learning Algo is: The algo. preferably chooses a Decision Tree which is the smallest. 

Why is this so when we can have bigger extensions of the tree which could in principle perform better than the shorter tree?
The bigger your tree is the more overfitting your model is. In machine learning, we always prefer a simpler model unless there is good reason to go for complication.