You can like someone for this or that, while still disliking them for something else. The two are not mutually exclusive. They can, and frequently do, exist at the same time. I don't get what's so hard to understand about that. Why must people flock to either black or white? Human beings and our minds are more complex than black and white.
The thing I'm most grateful to Mancini for, is his testimonies in court and the way he defended the club in 2006 when Calciopoli broke out. I maintain my stance to this day that calcio fans including interisti, are way too quiet about calciopoli and letting lies slowly creep back into tainting people's memories of the scandal. Every shirt or slogan or banner with which juve state "36 scudetti" that we don't deny, or argue against, is just letting falsehoods go unchallenged. Every article published which tries to slyly manipulate readers by deliberately focusing on non-issues (my favorite being "Inter should be relegated, but were saved by the statute of limitations") has influence over the public and adds another drop of poison to the pool of public opinion and knowledge. How many drops of poison before the whole pool is completely toxic? Mancini has always been upfront and clear about calciopoli, and he has defended our club from such lies, and that is the most likable and respectable thing about the guy in my eyes.
But similar to how Wenger eroded his legend to Arsenal fans over years of mediocrity, Mancini undoes that esteem I had/have for him with (what I consider to be) his ineptitude in managing the club, ineptitude I've spoken about many times and won't repeat.