Why do different calculators give different answers to 6 ÷ 2(1+2)?

The disagreement comes from notation, not from arithmetic itself. The expression $$6\div 2(1+2)$$ is ambiguous because some calculators treat it as $$(6\div 2)(1+2),$$ which gives $$3\cdot 3=9.$$ Other calculators treat the juxtaposition $2(1+2)$ as a grouped denominator-like expression: $$6\div [2(1+2)],$$ which gives $$6\div 6=1.$$ Professional mathematics avoids this by writing fractions: $$\frac{6}{2}(1+2)$$ or $$\frac{6}{2(1+2)}.$$ Those are different expressions. If a calculator gives a different result, it is usually because it parsed the ambiguous input differently.