There are several synonymous phrases and expressions that can be used in place of "show affinity." Some common alternatives include "demonstrate a fondness for," "display a liking of," "exhibit a preference towards," "embrace a connection with," "reveal an attachment to," and "evidence a bond with." Additionally, phrases like "have a strong inclination towards," "feel a natural kinship with," and "be drawn to" can also be used to convey the same meaning. It is important to choose the right synonym based on context to ensure clear and effective communication.