Meaning of 滅多な事では + Vしない?


I found a sentence like this: "滅多な事では物怖じしない". But the meaning of 滅多(careless)
make me don't understand this sentence. Then I searched something similar on
the website and I found this: "私は滅多に怒りません" which means "I rarely lose my
temper". So does it mean: " He rarely shows cowardice". Here the context of
the first sentence: "面倒見のいい性格で交友関係が広く, 滅多な事では物怖じしない胆力を持つ".




滅多【めった】 is rarely used outside fixed phrases today, but its original meaning
is something like "mindless" or "random", and by extension, "often" or "easy
to happen".

  * 滅多にVしない: "does not easily V" → "rarely V"
  * 滅多なことではVしない "does not V in random occasions" → "(specially) hard to make one V"

