Why don't animals(animal realm) commit suicide?
I'm not sure that they don't, not sure that it is never observed -- sometimes an old dog walks in front of a car for example, and is killed, and I wonder if they knew what they were doing.
But your question reminds me of a poem, by a non-Buddhist author, it's short and says:

Self-Pity
I never saw a wild thing
sorry for itself.
A small bird will drop frozen dead from a bough
without ever having felt sorry for itself.

It's a famous poem, striking, maybe worth considering from a Buddhist perspective.
I'm not even sure about that poem, though, not sure that it's true either: its author didn't always write kindly even about people (perhaps he was wrong about animals, too) -- it's hard to be sure of others' motives.
Animals sometimes feel sad, I'm pretty sure of that, and apparently mourn their dead; but perhaps self-pity depends on the ability to tell (or fabricate) a story about oneself: which, maybe, animals don't.