Hay Dan, thanks for your reply.
I tried to click different features in the attribute table and only one feature (the one always get highlighted in the attribute table no matter what I click in the scene) would let all features in the scene get highlighted.
As for other features, they wouldn't get highlighted in the scene after clicking in the attribute table, but with the Zoom To tool, I can zoom to the correct feature.
I checked the contents pane, and the layer is selectable.