The thyroid gland and all thyroid swelling move with the swallowing/deglutition because the thyroid is attached to the cartilage of the larynx by the suspensory ligament of Berry. Ligament of Berry also prevents the thyroid gland from sinking into the mediastinum.

Should thyroid move with swallowing?

The thyroid naturally moves up when you swallow. A normal thyroid can be felt when you swallow. If it is enlarged it can become easier to see when swallowing.

Does thyroid nodule move with deglutition?

Movement on swallowing has been emphasized as a highly specific feature of thyroid masses, but lesions in the vicinity of the thyroid can be displaced by underlying structures during deglutition, causing them to mimic thyroid nodules.