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The issue comes from the fact that the max(a,b) function is a Python builtin, that basically asks whether a<b and if not returns a. However, the symbolic expressions abs(x) and abs(y) are not comparable,
sage: bool(abs(x) < abs(y))
False
sage: bool(abs(x) > abs(y))
False
Hence, the max function will always return the first argument:
sage: max(abs(x),abs(y))
abs(x)
sage: max(abs(y),abs(x))
abs(y)
Here, you want to deal with the max wiewed as a symbolic expression, so you have to use max_symbolic instead:
sage: max_symbolic(abs(x),abs(y))
max(abs(x), abs(y))
sage: contour_plot(max_symbolic(abs(x),abs(y)),(x,-3,3),(y,-3,3))
