The right way to do it is:
x = A(1); y = A(2); z = A(3);
This [x, y, z] = A makes no sense because A is not a function. You can use more variables in the left-hand side of an assignment as the outputs of a function. If A is a variable, then you just can't do it.
Edit:
@horchler suggestion was to use a cell array to do it.
Perhaps then you can write:
A = 1:3;
A = num2cell(A);
[x,y,z]=A{:}
And that will work. First you convert your array to a cell, then use the assignment to define the x, y and z variables.
It is worth mentioning that this will do the trick for you, but that is not efficient. A cell array in MATLAB is much slower than an array itself and assign different elements of the array to different variables instead of using cell arrays will run faster though.