The cat is a predator
The cat is basically a predator and its behavior towards other species is typical of the hunter. Its typical prey is small rodents, birds and, in some habitats, fish, which it usually does not eat because they contain an enzyme that destroys thiamine (vitamin B1 essential for its health).
L predatory activity of the cat: an "exercise"
The cat catches fish, lizards and insects probably by pure "exercise" and by instinct . He does not need to be driven by hunger to engage in predatory activity; all cat owners know that even a chubby twink leaps like a spring in the presence of a prey, to capture and play with it, or give it alive as a gift to his "worshiped" human.
for apparently dangerous or larger animals, they are not natural prey for the cat, which can then be very cautious , friendly (if the context allows) or in case of need (eg mother feeling a threat to her children) of a great courage that allows him to confront, often victoriously, aggressors much larger and much stronger than him...
This article is it useful, does it address your problem?