Besides what you said (which I mostly agree with), that floating point calculations can at times be extremely counter intuitive, weird and totally inaccurate.

Besides what you said (which I mostly agree with), that floating point calculations can at times be extremely counter intuitive, weird and totally inaccurate. While a single floating point operation gives you the best possible floating point result, the error for two consecutive floating point operations is unbounded. They need to be treated carefully and people need to be aware of their shortcomings. You would be surprised how often I have seen even people here getting hung up over the fact that floating point numbers aren't behaving identically to real numbers.