The simple and most true reason I have come to is that its insecurity. The akali player feels that they should be winning due to how they are playing, that their team should be better etc. All the feelings of should bes and shouldn't are matters of insecurity in themself.
Losing a game makes them feel lesser, or worse about themselves and their time spent on the game, it feels ruined by others because their life is dictated by their beliefs of other people. They have to solidify their ideas in that its not their fault but everyone elses fault instead due to insecurity within themself.
If someone is actually happy with themselves, with their play and accepts the facts that they may lose or they may win then they will not ever flame anyone. The reason being is that they base a part of who they are as a person, their identity within the game. When that identity is devalued as in losing games on league, they feel as if they themselves are becoming devalued. In response they become defensive, blaming and negative in an attempt to convince themselves and everyone else that it is not their fault, and that this should not belittle their personal value whatsoever.
Its an entirely natural human trait unfortunately and it comes down to the very basics. If people could instead find value within themselves for other reasons aside from winning such as knowing they did their best, trying to find any single flaw they made and work to improve it, trying to teach and further team mates game knowledge in a calm manner rather than a hateful one then the flaming from these people would not happen.
I believe Riot has known this and is trying to change the incentives ie. the honor system/loading screens but most honors are recieved from winning and playing well as that is the main concern of the game and of the people in it. I could go on and on about it but simply put it is that the person is not happy with who they are unless they are winning, and then they get defensive to protect their feelings on the matter. Their sense of security in themself comes from winning the game, and their priorities are skewed. In reality its actually pretty sad, and I simply feel pity for the people who are in that state of mind so far that they feel the need to belittle peoples lives/value in a painful attempt to protect their own shortcomings.
I won't lie in that I myself have had these shortcomings or insecurities and have raged at games although not very often, and it is something that I am consistently trying to better myself at not only in league but just life in general. Not getting upset by expectations and reality is a lifetimes worth of work for anyone. I hope I shed some light on it and I apologize for the massive wall of text.