Why did Chile not support Argentina during the Falkland Islands War?

Chile did not support Argentina during the Falkland Islands War primarily because of a tense territorial dispute between the two nations regarding islands in the Beagle Channel.2

This long-standing conflict, which had nearly led to war between Chile and Argentina in 1978, created a state of alert along their shared border. Consequently, the perceived threat from Chile forced Argentina to keep the majority of its elite military troops stationed on the mainland, distant from the Falklands theatre, rather than deploying them to the islands. While most other Latin American governments sympathized with Argentina during the conflict, Chile remained a notable exception due to these regional security concerns.12