We have a new player which is very unsatisfied with the available avatar options because they absolutely do not fit his character concept. Because of this he want to put no background in Avatar so that he has not this interference and we now ask us, is the description of the avatars in M20 just the extremes or stereotypes or is automatically a mage on of those four? Because from what we understand Avatars are a part of the mages personality so the mage need to be like one of the avatars. Or can it be, that they are like the roommate which speaks out what you know and want you to strive for better?
No, an Avatar need not have the same personality as their mage. Depending on the mage's paradigm is, an Avatar may be perceived as a primal spirit guide, one's higher purpose, their "better self," or the "devil on their shoulder." The mythology of the game proposes that Avatars may be shards of a universal Oversoul that reincarnates from mage to mage, and that means they can be as alien or as personal as desired.
The Essences described on page 267 of the M20 corebook give these archetypes form and offer players and storytellers a way to introduce them into a game with a personality, but they are strictly roleplaying guides. In a real sense, they are stereotypes.
It's also worth noting that the Essence of an Avatar has no mechanical effect. You can easily pick one that sounds evocative and ignore it thereafter. Taking a high rating in the Avatar background indicates a desire to play more with this element of the game, but that's optional.
In fact, given the sorts of common personalities Avatars are described to have, it's highly unlikely that many humans can be fully in tune with them. Furthermore, many STs GM games where the one of the major themes is the struggle between an Avatar pulling in one direction, and the mage wanting to go in a different one - it's a very fruitful soil for plots and drama.
Finally, perhaps one of the more drastic examples of mismatches are the Technocrats and their Avatars. Surely you would never expect near-eternal Avatars to have personalities anywhere near similar to those of Technocrat characters?