The Baal Shem Tov (Parashath Hukkath) explains that the mitzwah of Parah Adumah is rooted in hubris. In order for a person to begin his journey towards truly serving HaShem s/he must start by pursuing Torah and Mitzwoth for secondary reasons, reward, prestige, or the like. This is the hubris, that a person who is so powerless and insignificant could be doing 'favors' for HaShem who is boundless and all-powerful, such that they should be deserving of any reward. Later, when one is well on his or her way to serving HaShem we need to flee from any hubris which might taint our true and earnest service of HaShem for its own sake. This is the nature of the Hubris, like the nature of the Parah Adumah that it purifies the impure, those far from HaShem, and causes those who are pure and close to HaShem to become impure.
Similarly in our daily mitzwah practice, the Baal Shem Tov, goes on to explain, we must overcome the initial resistance of the evil urge in order to perform a mitzwah. The Yetzer Hara says: "You aren't worthy to perform such a lofty mitzwah." You must reply with hubris and assert your worthiness, and undertake to do the mitzwah anyway. Once you are involved in the mitzwah, (and this is the key point) any hubris will taint that mitzwah. We must be careful lest we think that our mitzwah makes us better than those not involved in the mitzwah.
It's clear to see how easy it is to mess up a perfectly incredible mitzwah by letting it go to our heads -- but if we didn't have a little ego when we started, we would never have taken the first step. What was impure becomes pure, and what is pure can easily become impure, through the very same mechanism.
That's the root of the Parah Adumah in every mitzwah.