Yeah... no math class I had in grade school ever tried to teach us that 1 wasn't a number. (And if anything, 0 was what got treated as a outlier or "base"; kind of like the point that separated positive and negative numbers because 0 itself technically wasn't positive or negative. Anyone remember those number lines...?)1 isn't a prime number because its not considered to be a number at all. its considered to be "The Quantifier" or "The unit" around which all numbers or "integers" are based.
Granted, like I said I never was in any particular advanced college-level math class, so that could be why.
To me, those are two entirely different statements. "A prime number is divisible by itself and 1" would indicate that literally every number is a prime number. The latter statement would not."A prime number is divisible by itself and 1" is the simplified version of "A prime number is a whole number with exactly two integral divisors". 1 doesn't have two integral divisors so it can't be a prime number.
Kids at schools are given simplified information because few want to actually learn anything, those who want to learn more usually ask questions and nothing prevents them from acquiring further information which brings clarification.
You can't really blame your teachers for not understanding if they gave you the simplified definition, I asked questions when I wasn't understanding something even if it sounded idiotic to my classmates who always got lower marks than me.
To me, I saw the number 1, saw that it is potentially divisible by itself (1) and 1 (and no other numbers), and thus concluded that it should be a prime number based on the whole "only divisible by itself and 1" thing that I was consistently taught in my math classes. I didn't "not understand" anything, therefore I had no questions to ask. I never had any reason to question that knowledge until many years later, in FF12 playing a low level challenge, when I learned that being level 1 actually protected you from being hit by Zalera's Prime Level Death (indicating that 1 actually was NOT a prime number).
I (and the rest of my classes) was fed information that misled and didn't paint the whole picture, simple as that. So yes, I will blame my instructors for this one. Your attempted "well, the kids don't care about this stuff anyway, so why should I bother trying to teach them effectively" defense doesn't fly with me, sorry.
If a "simplified" definition leads to misunderstandings like mine, maybe it shouldn't be used in an educational setting.