Question: Cow milk is fermented with kefir grains, and little amount of alcohol emerges during fermentation. The resultant drink is called kefir. Additionally, there is a drink called kombucha prepared by reproduction of kombucha yeast and containing low rate of alcohol. Both kefir and kombucha are reported to have a variety of healing properties for many diseases. Is there anything wrong with consuming them for medicinal purposes?
ANSWER
Today there are a lot of medicines replacing kefir and kombucha, so there is no dire need to consume them. If a pious Muslim doctor says, "Kefir [or kombucha] will have a beneficial effect on your illness. There is no other medicine that is permissible," only then will it be permissible to drink it. A hadith-i sharif says:

(Every drink that has gone through the process of ihtimar [production of alcohol by fermentation] is haram.) [Abu Dawud]

Let us see how the abovementioned hadith-i sharif is explained in fiqh books:

When any one of honey, figs, barley, wheat, corns, millets, plums, apricots, apples, or the like is kept for a while in cold water, even if the mixture has not been heated, it produces alcohol and becomes like beer. Because beer has a bitter and pungent taste [as it contains alcohol], it is haram, according to Imam-i Muhammad, to consume it, regardless of the amount consumed or the purpose for consuming it. The fatwa was issued based on this. It is haram in the other three madhhabs, too. It must not be construed that the beverages in question are classified in the same category with respect to their chemical formulas because Muhammad ‘alaihis-salam was not sent to humanity to teach them science or chemical essences of substances, but to teach them the Islamic rules pertaining to the usage of substances. When milk from a mare or from a cow is fermented and assumes a pungent taste, it contains alcohol like beer. The former one (the one from a mare,) is called qumis (koumiss or kumiss), and the latter is called kefir. Consuming them is haram. (Se'adet-i Ebediyye)

Question: Yoghurt made of milk is not haram. Why is kefir made of the same milk haram?
ANSWER
Islamic rulings must not be judged based on mind and reasoning. What you have said is similar to saying "Why is vinegar made of grape permissible while wine made of grape, too, is impermissible?" Islam cannot be based on mind and logic. As many religions as the number of humans would emerge then.