Of course, squirrels don't only make chattering noises and calls to defend from predators. There are other times like during courtship when squirrels can be incredibly loud and vocal. Sometimes you'll hear a chattering squirrel noise that again sounds very much like an alarm.

Do squirrels chatter their teeth?

Social interactions, especially those related to the defence of resources or kittens from interlopers and predators, often involve sound. Indeed, Red squirrels are known to produce both loud and soft “chucking” noises, a vehement “wrruhh-ing” as well as various moans and teeth chattering.

Why is this squirrel making weird noises?

Squirrels establish and defend home territories that contain their food sources. ... The rattles appear to advertise the defending squirrel's presence, and the screeches convey a threat to the intruding squirrel. Lair interprets a barking call as a signal to another squirrel to reveal its intentions.