Feeling is a reaction to a stimuli.  There is no implication that thinking must be involved at all for feeling.  This does not exclude the possibility that thinking could occur somewhere down the line.  If you are shown a picture of dead child you will have an automatic reaction.  If I switch to a picture of a kitten snuggling with a puppy, once again you will have an automatic reaction.

The problem is that most of the weak-minded, non-analytical types get to the "feeling" and progress no further.  Lets take the famous example of Alan Kurdi, the Syrian boy dead on a beach whose photograph was flashed all around the world.  The resulting "outrage" inspired hundreds of thousands or even millions of people to vent their "feelings" and "demand" that an unlimited amount of "refugees" (as they were called) be allowed to flood the shores of Europe.  Here are the "facts" that were omitted from the story.  The boy was not "fleeing war", he was living safely in Turkey for quite a while.  His father was involved in people smuggling and was therefore responsible for his son's death. The father wanted to go for free dental treatment in Canada, not flee war.

Now what has happened?  Just 1.4% of migrants arriving in Italy in 2017 are "Syrian Refugees" and the monster percentage are economic migrants.  This is what happens when feelings trump facts.  Outrage is directed in an erroneous way.  

There are many other examples that I could have chosen.  However, I will conclude with a refutation of your first sentence.  Feeling is feeling.  Critical thinking using evidence and facts is something else altogether.