Rebbi meir forces the 2 remaining of 4 brothers to give chalitza, in order not to possibly be Mevatel the Mitzvah of Yibum (if the remaining brother dies before doing Yibum)...
i don't understand this logic: he will not allow at least one legitimate yivum and force 2 chalitzas.
imagine the 2 brothers are ready to do yivum and we don't allow it because one of them may die. it does not make sense the "main" mitzva is yivum and we don't allow it to take place? there must be a different explanation than what is on the surface.
1) We see from here that Chalitzah is also an important Mitzvah and by doing Chalitzah it may be that to a certain extent one accomplishes as much as Yibum accomplishes. However, this is not a simple matter and, in fact, the Ritva writes something very similar to your logic, as I hope we will see later on, b'Siyata d'Shemaya.
2) However, let us first look at the Ramban. He relates to the question of Tosafos (DH Dilma) who asks that we generally are not worried that someone will die, so why here are we concerned that the other brother will die? The Ramban answers that when there is nothing to lose, the Halachah is actually concerned that someone will die, while all the places that we say that Chazal are not concerned about dying relate to scenarios where there is some need not to be concerned about death. For example, if a Kohen gave his wife a Get and said that the Get will be valid an hour before he dies, it is not possible to be worried that he will die, because this would mean that his wife may never eat Terumah. If we would require the Kohen Gadol before Yom Kippur to prepare another wife because his present wife might die, we would have to prepare for him an unlimited number of wives, because if we are worried that one wife might die we might just as well be worried that a number of wives might die.
3) The Ramban then writes what is relevant to our topic: "Since Yibum and Chalitzah are equal, we do not bring ourselves to any doubt by abolishing a Mitzvah" if we require Chalitzah instead of Yibum.
Hence, according to the Ramban, our Gemara is concerned that a brother might die because nothing will be lost as a result, because one achieves just as much with Chalitzah as one does with Yibum.
4) However, the Ritva writes that this idea is not sufficiently clear (and I think that this is what is disturbing you), because the Gemara later (21a) states that if one does Chalitzah instead of Yibum, one has performed nothing. The Ritva adds that the answer of the Ramban can work only according to Aba Shaul who maintains (39b) that the Mitzvah of Chalitzah takes precedence to the Mitzvah of Yibum.
5) I would refer you to the very lengthy notes on the Chidushei ha'Ritva published by Mosad ha'Rav Kook. In the "Milu'im" at the end of the Sefer, Rav Yaffen writes a lot on this question. In chapter 10:7, he cites Mefarshim -- including the Netziv in Ha'amek She'elah 154:1 -- who prove from our Sugya that Chalitzah is a positive Mitzvah, not merely a process necessary to allow the Yevamah to remarry.