I think folks tend to see more - ONLY - the murdered President, and less the policies and things he supported.
The fact that he served honorably in WWII didn’t hurt him either, what with the whole PT-109 incident (although how much of that is real versus fabricated is up to anyone guess as well; I’ve heard both sides of that story).
A very wise man and dear friend of mine once told me - “You come to a point where you realize that most of what you were taught just might be bullsh*t...” And regarding history - FDR, etc., - he was correct.
It's worse than that, its a cult of personality. For example, President James A. Garfield was likewise tragically murdered in his 40s before he had accomplished anything as President (his mother even saw him murdered in front of her), and UNLIKE JFK, Garfield was an actual conservative and a decent guy. But you never hear people on the right or left speak in revered tones about what a heroic, beloved figure Garfield was, or claim he was killed because he was planning to expose the corrupt establishment in this country.
The mainstream media has convinced ALL Americans, regardless of ideology, that JFK was some kind of revolutionary superhero, and anyone who disputes this propaganda on the right or left is immediately attacked. He was a mediocre leader who has become a sacred cow whose "great legacy" cannot be disputed, like the Kim Jong clan is in North Korea.
What I find very interesting is the SAME folks who constantly repeat the heroic patriotic savior JFK myth and proudly repeat the "Republican states are RED!!!" propaganda are the ones who balk at the media saying the confederate flag and the confederacy itself represents racism and slavery, crying "WE CAN'T LET THE MEDIA DEFINE THINGS FOR US!!!!"
The irony is delicious.