You have started your manipulation. If you start with "-3 not equal to 3" it is not anymore the same as starting with

Why not?

Because

has two values:

is not only equal to +3 but also to -3.

And let's see now where we end up with this knowledge, taking into account your advice "no need to start with a radical sign":

You said that squaring both sides of an equation is not always a valid algebraic step. But I have always exposed the mainstream lies and manipulation. And perhaps the real reason for your error is something else. Maybe you should not start with the error

.

I don't end up with nonsense. You end up with nonsense:

does not mean +3 = -3

Your manipulation says the opposite:

According to you

means

if

because you are trying to force the above into

but without understanding that there is no error here:

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