I don't think anyone is advocating the sacking of him in reality. People are simply venting their spleen about a piss poor performance from the team and a lack of direction from Rodgers that we seem to have carried for some 13 or so games now. That's perfectly fair and not at all hyperbolic. He needs to see the error of his ways quickly though otherwise frustration will turn to sourness and anger. That's when things quickly go badly wrong for a manager.
There's no doubt we need a fresh look at this team. There are some cracking players but we won't ever get the best out of the likes of Maddison, Tielemans, Vardy, Perez etc... unless we invest in some proper support for them. We must let the likes of Choudhury, James, and Iheanacho (controversial I know but he's never going to be good enough for a side wanting CL qualification year in, year out) go I'm afraid as well as the ones who just don't seem to give two shits like Chilwell and Gray. We can do so much better than this rabble but we need wise investment. We need to go back to looking at players like Cantwell, Lewis, McGinn, Grealish, Digne, Calvert-Lewin etc... young(ish) players with desire and a great work ethic, whilst maintaining the older heads like Evans, Fuchs, Morgan and even Albrighton et al to help when the chips are down and players need that little bit of experienced advice.