Why has hashem given us a mitsva without a reason and one which is impossible to understand. All the others even the 'chukim' at least Solomon understood. This one even he didnt that shows it is impossible to understand the reason. Although moshe rabainu did he was a 'special' case. Why have mitsvot where one can never know the reason. The mitsva of poroh aduma is the only one where some on earth with his limited 'sechel' cannot understand. All the others can be. So the question is since all mitvot can be understood as King Solomon has proved, and that is really are purpose in life to try to understand them, why have one which cannot be understood.
The way I understand it is that mitzvos which are chukim show our true belief in Hashem. Mitzvos that we do understand one can say we are doing them because they make sense to us but if they didn't make sense we wouldn't do them.We as Jews treat all mitzvos alike whether we know the reasons or have the slightest clue , we keep them no matter what and for that reason we have many mitzvos which are truly unknown to see who believes and trusts in Hashem.(I have seen this reason brought down in a sefer ,don't remember where.
The more philosophically-inclined rishonim apparently didn't think this commandment was not understandable. For instance, Rambam explains it in Guide for the Perplexed 3:47:
The red heifer is called a sin-offering, because it effects the purification of persons that have become unclean through the dead body of a human being, and enables them to enter the Sanctuary [and to eat of hallowed things]. The idea taught by this law is this: Those who have defiled themselves would never be allowed to enter the Sanctuary, or to partake of holy things, were it not for the sacrifice of the red heifer, by which this sin is removed; in the same manner as the plate [which the high-priest wears on his forehead] atones for uncleanness, and as a similar object is attained by the goats that are burnt. For this reason those were unclean who were engaged in the sacrifice of the heifer or the goats which were burnt, and even their garments were unclean. The same was the law in the case of the goat that was sent away [on the Day of Atonement]; for it was believed that it made unclean those who touched it, because it carried off so many sins.
R. Saadia Gaon explains it in Emunot V'Deiot 3:10:
In the eighth place, thinking about the case of the red heifer, one might wonder how it could have been ordained that this heifer was to purify the unclean and defile the pure. Our answer hereunto is that it is by no means extraordinary that one and the same thing should roduce two opposite effects, depending on the nature of the body that encounters it. For we note that fire liquefies lead while it solidifies milk, and that water moistens the wood of the pine while it dries that of the sycamore. We find, furthermore, that good food is beneficial to the person who is hungry but harmful to him that is sated, and that choice medicine might be of benefit to the sick and yet do harm to the person who is in good health. Hence it is not strange that the same thing should have the effect of purifying the impure and defiling the pure.
(Rosenblatt translation p. 178)