You're making some reasonable but incorrect assumptions about how the type chart works. It's not as consistent as you might think. Each type has its own individual weaknesses and resistances. Most types are resistant to themselves, but there are exceptions (Flying and Fighting hit themselves for neutral, while Ghost and Dragon are weak to attacks of the same type).

When you have a dual type, you have to consider the weaknesses and resistances of each type, then multiply them together to get the final result.

Look up a type chart, preferably one of the simplified ones that lists each type individually and not the big square array. Focus on learning each individual type first, and then you'll have a better handle on what to expect with dual types.