Power Of Milah

Why does the Torah mention the mitzvah of milah after describing the tumas ladeah-tumah of birth?  Why would this mitzvah be mentioned in the middle of laws of tumah?  The Or Hachaim explains the necessity of bris milah stems from the sin of Adam.  Through his sin the world became contaminated and the manifestation of this in the body is the arlah.  Birth pains and the subsequent tumah also stem from this contamination.  Therefore, after mentioning the tumah of birth it mentions milah because they both stem from the tumah that exists because of the sin of Adam.  The job of milah is to fix up this contamination in the world.  This idea is reflected in the Gemorah Sanhedrin (38b) that says Adam nullified his milah  What is the Gemorah teaching us?  The Gemorah is alluding to this idea that his sin ruined the perfection that existed in the world.  

This could be the explanation of the Ollalos Epraim brought in end of responsa of Rabbi Akivah Eger 42, that understanding Torah can only be accomplished after milah.  Why is it milah a necessary prerequisite to understanding Torah?  In order to understand Torah, one must remove the contamination that exists within himself.  

The Gemorah (Shabbos 132b) says a derash on the word bayom that bris milah is performed even on Shabbos.  The Or Hachaim asks why is this halacha learnt alluded to here and not by mitzvah of milah given to Avrohom?  The Maharal (Nedarim 31b) explains the reason why milah overrides Shabbos is because Shabbos is the completion of tevah.  However, milah is done on day eight for it is above tevah.  Milah is higher than Shabbos and therefore overrides it.  Possibly this above tevah power can only have an effect on the world post-mattan Torah.  It is only after the giving of the Torah that a mitzvah can have an effect on the world as discussed here.  That’s why it is only the milah done after mattan Torah that can override Shabbos.