I kinda understand the steel thing, ice as a material in general is weaker. A steel skyscraper stands taller than an igloo and an icicle isn't a suitable weapon against a steel dagger.
Fighting strikes me as an odd weakness for ice types though. Rock types being weak to fighting might makes sense since people doing martial arts might break bricks but punching ice sounds like a strange thing to do, my hands get numb just making a snowball without gloves.
You ever seen Rocky IV? Rocky going into the snowy mountains to train in the ice.
Fighting > Ice