I think you're going the wrong way with this. Will himself certainly isnt hated. Denzel isnt hated. Its intellectually lazy to say that because someone isnt liked its automatically because people are jealous. Thats the 1% answer for everything that people reject.
Concerning Jaden, its easy to see why he is disliked. Will is doing way more that "putting him on", he is shoving him in the public's face in ways that far exceeds his son's talent. Putting him on would be to put him in smaller roles to allow his son to develop his talent, and to also develop a fan following. Putting Jaden in starring roles in big budget features as a 14 year old, and making it clear he is only there because of who his daddy is, is a recipe for disaster and thats already materializing. I thought Will was more savvy than this.
And the quickest way to get the public to hate you is through over-exposure, and Jaden is being severely overexposed. Every where I look, there he is. If Jaden isnt rapping, then hes being interviewed. If he isnt being interviewed, then he's dancing on a show. If he isnt dancing on a show, then hes starring in blockbuster movies. Hes creating a natural backlash for Jaden, and its not like Jaden is this awesome talent. Will is being a stage dad here.
Will wanted to create the black justin beiber. Not only did the fans not take to this (white girls want lil blonde boys as sex symbols, and black girls dont identify with him), but they clearly just dont like him that much. Will keeps pushing harder, rather than having Jaden fall back. Hes killing his kid's career, and you guys keep talking about this "kaks have done it too", but I cant remember an example of a famous father pushing his kid so hard into the limelight, with such poor results. Will is dead wrong.