A genetic predisposition towards being afraid of predators. The assumption is that if you have 100 mice, and 50 of them show signs of being afraid of cats, then you breed those mice to produce another 100, noting the pairs that produced them. You can then see how many of the offspring are afraid of cats, and select that group to produce the next generation.

Some of the fear of cats will be learned behavior, some of it will be instinct. It could also be that the ability to learn the behavior has genetic links (think naturally smart mice). If you keep this cycle going, eventually you have a group that should be higher than your initial 50% fear rate. It's possible that you can't selectively breed for this, but it's also possible that you can. This is in some ways the inverse of how humans domesticated many different species.

In species where adults raise their young, the young are typically hanging around with the parent for a while between when they're able to walk/fly on their own and when they reach full maturity.

The parent sees/smells a predator and flees/hides; the young flee/hide with it. They learn that the response to the stimulus associated with the predator is to flee/hide.

By teaching? Parent demonstrates behavior, child learns. Same as in a human society.

Not speculation - emerging but well supported science: https://en.wikipedia.org/wiki/Animal_culture