From the Editors of The Daily Cat
The behavior you describe is called redirected aggression. It’s when aggression is inflicted upon an individual or group that did not provoke the initial anger. We humans do it all of the time, such as when a spouse or roommate picks a fight with someone after having a bad day.
It sounds like your cat is experiencing many bad days -- or at least moments -- watching the neighbor cat march onto his home turf. Cats are extremely territorial and will often try to “push buttons,” expanding into another cat’s area that might be desirable. Feral cats often do this to house kitties. If the latter is left outside at night, in particular, roaming feral cats may try to attack and scare off the home cat, acquiring the area for themselves. That is one of many reasons why you should not let your cat outside, unless he has a leash or other protection.
You probably cannot prevent him from spying on this other male cat. The Humane Society of the United States offers these tips for dealing with feline aggression:
With any luck, your neighbor will also want to improve his or her cat’s safety by making him indoor-only too.