It's not the pinion that is weaker it, its the stress exerted onto the teeth that is higher. With a numaricly higher gear ratio you have less pinion teeth, there for less contact withthe ring gear. When there is less pinion contact with the ring gear the force exerted onto the pinion teeth rises and causes the failure. The more teeth in contact the more the load is spread

Just like a wide tire vs nerrow. The nerrow tire has more pressure per square inch than the wide one because of the size of the contact patch.