Why 0÷0 is math error? Ain't the answer 0? I know all numbers cannot be divided by 0, but...why? Whywhywhy?

When you first started learning division it was interpreted in certain ways to make sense to you as a 3rd or 4th grader
12 divided by 3 was explained to you as a grouping problem
How many groups of 3 can be made from 12? ... and you may have even used sticks or disks to do the grouping.
||| + ||| + ||| + ||| = |||||||||||| <<< I hope that is 12 sticks
so 12 divided into groups of 3 will make 4 groups
12 divided by 3 = 4

so think 5 divided by 0 ... what does that mean???
... each group is to have 0 in it ... how many groups can you make with none left over??? there is no number answer, so it is called undefined. Math likes to be consistent, so 7 / 0, 15 / 0 , anything / 0 is undefined because there is NO NUMBER ANSWER for any of these ... notice I was very specific ... NO NUMBER ANSWER.
You may want to say 'infinity' but infinity is NOT a number. Infinity is a concept of something so large that you can never get there by counting.
... There is NO NUMBER ANSWER ....so that is just shortened to UNDEFINED. Anything divided by 0 is always undefined ... anything, including 0 itself. ... You can argue about it all you want, but there are rules in math. You don't get to make up new rules. You must learn maths rules.
The rule [ANY NUMBER] divided by 0 is UNDEFINED.

0 divided by 0 is an expression that is undefined, meaning there's no answer or it doesn't make sense. Think about it this way:

Take the number 1 and divide it by an integer that is greater than 0, say 5. This would be 1/5. Take a smaller integer like 4 and divide 1 by this number. This would be 1/4. You can already tell that the number is getting larger and larger as the denominator or divisor is getting larger since 1/4 is smaller than 1/4 but 5 is larger than 4. Take a number like 1 now. 1/1 is 1, which is larger than 1/5 or 1/4 even if the divisor or denominator is smaller than the denominators or divisors of 4 and 5. You can even start dividing by decimals, 1/0.1 is 10, 1/0.01 is 100, 1/0.001 is 1000, 1/0.00001 is 10,000, and so on. As the divisor or denominator gets smaller, the quotient gets larger. Since there is an infinite amount of numbers that are larger than 0, 1/0 has to be larger than any of these infinite quotients, showing that any number divided by 0 is infinity. Most mathematicians refer to any number divided by 0 as undefined rather than infinity since it would not make any sense to divide by 0 anyway, so any number divided by 0 is undefined, including 0/0.

You can't divide anything by zero. Including zero.

One could claim that the answer is 1 since you're dividing a number by itself. But then as you claim, since the numerator is 0, the quotient must be 0.

So you have a conflict where both are right, therefore, neither is right.

Here's the real reason.
There are really only 2 operations: multiplication and addition.

Division is DEFINED as multiplication by the inverse. The inverse is what you multiply something by to get 1. E.g., the inverse of 2 is 1/2 because 2 x 1/2 = 1.

So 10 / 2 means 10 x 1/2 = 5

0 has no inverse. There is no number n such that 0 times n = 1.
Therefore division by 0 is undefined. It doesn't exist.

If you want to defined division like this:
a/b = c if and only if bc = a
then again if a is not 0, a/0 is undefined because there is no c such that 0c =a

If a does = 0, then 0/0, per this definition, could be anything, 0x5 = 0, 0 x 13 = 0, etc. With this definition, we would say 0/0 is "indeterminate."

Because by asking for the value of 0/0 you're asking how many times you must add zero to itself to get zero:

Obviously, 0=0, so you might say 0/0=1
But 2x0 = 0, so you might say 0/0=2
But 3x0 =0, so you might say 0/0=3
and so on

so you can't make up your mind and that's why most of the time 0/0 is simply not defined. However, sometimes you'll see a formula of many variables where some numerical assignments of the variables give 0/0, but the formula will come with a disclaimer such as "where 0/0 is taken to be [some number]".

0/0 is indeterminate.
Let x = 0/0.
Multiply both sides by 0.
0x = 0
0 = 0
x can be any number. Since there is more than one possible solution for x, 0/0 is indeterminate.

Anything divided by 0 is undefined. There's two sides to consider here. Numbers really close to zero divided by themselves would equal 1. For instance 0.1/0.1 = 1, 0.01/0.01 = 1, 0.001/0.001 = 1. So following that logic it would make sense that 0/0 = 1, right? But at the same time, anything divided into 0 is 0. So 0/0.1 = 0, 0/0.01= 0, 0/0.001 = 0, so by that logic... 0/0 = 0. Since they are both valid arguments, mathematicians have just left it as undefined since it cannot be 0 and 1.