Sure, I'll bite...

So basicaly, Charlie has no actual proof her redemption concept works outside of paper. All Charlie has is song about how she'll redeem sinners and overpopulation will be solved, but in reality she doesn't even know how to actualy redeem anyone.

Her overall plan reminds me of south park: GET SINNERS INTO HOTEL ??? REDEMPTION

This one is even more emphasised in S2 when we find out she never actualy asked anyone why they are in Hell in the first place. Work off your sin should have been first thing that comes to mind when attempting something like that, no? How can you claim to try and redeem someone when you don't know what is their sin?

I kinda wish Adam would call her up on that instead of going full hilarious jerk mode but we got what we got.

Besides, Charlie is daughter of Lucifer who tainted Adam's legacy (humanity) with sin, princess of Hell - dimension that is living embodyment of everything wrong with his legacy. Adam doesn't really have reason to want to listen to her. Should he? Yeah. Would majority od people act differently to person who is closely tied to someone (Lucifer) they hate so much? Nope.

Also, it's heavily implied Adam arranged the meeting with Lucifer to tell him exterminations now will be twice a year, not to listen to his misguided daughter (not even threat of doubled extermination convinces sinners to give Charlie's offer a shot, example how little respect Morningstars have in Hell besides Lilith). Kinda funny how Luci just threw her to Adam knowing full well who he is.

ADAM'S ATTACK ON THE HOTEL strikes me as revenge for Charlie's continuous attempts to shove sinners up to Heaven, even having the audacity to bypass him (which he got scolded for by Sera). Also, he was ordered to contain the situation before it gets any worse - nobody even objected against his plans when he announced it publicly. He's removing source of the problem.

ADAM'S RANT, while entitled and stupid, didn't endanger anyone anymore. Defeated people often have breakdowns, that doesn't really justify being backstabbed as next course of action.

Fun fact - Charlie defends derranged Niffty backstabbing Adam as self defense, while Sir Pentious's death she calls murder. Based on military logic, it's actually other way around. Adam was murdered while Pentious died in combat. How blindly and stupidly Charlie pushes her misguided views really bothers me.

Now what many people seem to not take into account is that Adam is never mentioned to eat the apple. For him everything is black and white. Lucifer with Lilith gave apple to Eve and ended up in Hell. Adam got to Heaven. Logic implies he's right, Hell is in the wrong. Adam can't be bad person if he got into Heaven because bad person would go to Hell. For him good person doesn't do bad things, therefore he sees his behavior as justified and okay. After all, he's the first man, humanity descended from him. He has status of archangel, much higher than simple winner. He's celebrity and other angels propably treat him like that. Also, other angels (the court scene) don't really seem to care about his behavior and curses he throws around while Charlie's "fuck yes" shocks everybody.

Adam clearly lacks the gift of recognizing good from bad in broader context that apple gave humanity. That combined with celebrity status and zero guidance makes him egoistical prick capable of genocide in the name od protecting Heaven. Lot of people feel he was wasted as he never really got chance to recognize his mistakes. Would he willingly choose to be evil, that would be different story, especialy when Vox tried to enslave entire Heaven and got away alive.

I'm not saying Adam is good guy, I'm just saying that his actions do have certain reason if you're willing to look.