Why should we use less on fewer occasions?

Because fewer is correct for countable nouns: cats, cars, pens. Less is used where the noun is 'uncountable' or does not have a plural: milk, money, air. This simple rule is often unwittingly broken, particularly where there is an irregular plural noun: person becomes people and so there fewer not less people.

A video explaining the fewer less/rule for second language learners is here