Assumption: The meat you buy at the local outlet is kosher.
Assumption: The milk you buy at the local outlet, even if lacking a kosher label, is inspected by the US Department of Agriculture (USDA) to assure it's not adulterated.
So why the big fuss about "kosher for Passover" labels?
According to Rabbi D. Marc Angel, "Questions arise if these things (meats) were prepared, cut and packaged before Pessah using hametz implements. As a rule--and certainly from a Sephardic perspective--if these things are bought before Pessah there's no problem, since whatever tiny amounts of hametz might be involved would have been annulled by a ratio of sixty to one. That rule, though, only applies before Pessah. For things bought on Pessah, hametz is never annulled no matter what the ratio."
The "operative words" in Rabbi Angel's comment are "from a Sephardic perspective."
Chabad's Rabbi Yehuda Shurpin holds that "the problem arises when foods are being processed -which almost all foods nowadays are. For even if a small amount of Chametz gets into the food it is rendered not kosher for Passover."
Dairy products - even milk - is a bit more difficult issue than meat.
The USDA assures us, through on-going inspections that the milk we think comes from cows (or goats) actually does come from cows (or goats). We don't have to be concerned that someone is adding milk from a non-kosher animal (camels, for example).
But what the USDA does not do is assure us that the ADDITIVES - the vitamins and other things put into the product to keep us hopefully healthy are kosher for Pesach. The "fly n the ointment" as it were, is alcohol, often used to "cut" ingredients that are used to enhance a basic product, e.g., the Vitamin D additive. Someone has to check the source of the alcohol, and most kashrut agencies apparently don't go that deep into the processes.
Beyond the additives, Orthodox Union Kashruth Division's "Web(be) Rebbe" reminds that "dairies do not just do milk anymore. They package all types of drinks. Chocolate milk, soy drinks, rice drinks... There are dairies that bottle chicken soup! (Very rare)."
What if you fail to find kosher for Pesach milk?
As Rabbi Angel said about meat, Rabbi Alexander Haber said about milk: "Milk contains additives like Vitamin E which are Chametz. If bought before Pesach these additives are nullified by the 1/60 rule. Chametz cannot be nullified on Pesach itself." Milk lacking a kosher for Pesach label, to be used during Pesach must be purchased before the search and destruction of hametz.
Milk products, such as yogurt, present their own problems.
Rabbi Yosef Landa of the CRC, notes that "other items do require (a kosher for Passover certification), because of various ingredients in these products, such as the rennet and vitamins. Yogurts have all sorts of ingredients in them. In addition these are processed while hot, and the equipment can be used for non KFP items as well."
Rabbi Landa also wrote that "Just because the product bears a K4P symbol doesn’t necessarily mean that it requires it, just as many year round kosher products bear kosher symbols even though it is not required, salt for example. Manufacturers like to put the symbol there, since not all consumers know what requires a symbol and what doesn’t. In fact fresh or frozen whole meat or chicken does not require special kosher certification for Passover. (Rabbi's emphasis above.)
A note about sodas/colas.
Why, I asked myself, would a Sefardi need to worry about colas being kosher for Pesach. The Ashkenazi needs to be concerned because the bottlers often use corn syrup as a sweetener; corn is kitniyot and kitniyot are forbidden to Ashkenazi - but not Sefardi Jews.
Turns out that, like milk, there are ingredients in colas that may be kosher but not "kosher for Pesach." I'm not a chemist or a food scientist so I'm not privy to exactly what might be a problem for Sefardim. I am a bit disconcerted by the major certification agencies in the U.S. - OU, CRC, Star-K, OK, etc. - have blinders that allow them only see things the Ashkenazi way. Perhaps that will slowly change. In France, the primary kashrut agency includes a line on products containing kitniyot that reads something like "permitted to people who consume kitniyot." Bravo!
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Blogger's note: The spelling within quotes is the quoted author's and reflects the problems of trying to transliterate Hebrew to Latin characters. Chametz, chometz, hametz, hames - it's all the same when read right-to-left.