Here is a step-by-step proof (yes, a proof that really is valid!) that happiness depends partly on grammar.]
For genuine thinking, we need words. (By “genuine thinking” I mean as opposed to merely being conscious of feeling hungry, tired, angry and so on and wanting to do something about it; in other words, anything that animals cannot do.) Thinking cannot be done without words.
If we do not use words rightly, we shall not think rightly.
If we do not think rightly, we cannot reliably decide rightly, because good decisions depend on accurate thinking.
If we do not decide rightly, we shall make a mess of our lives and also of other people’s lives to the extent that we have an influence on other people.
If we make a mess of our lives, we shall make ourselves and other people unhappy.
In summary of the proof: grammar is the science of using words rightly, leading to thinking rightly, leading to deciding rightly, without which -- as both common sense and experience show -- happiness is impossible. Therefore, happiness depends at least partly on good grammar.