Why is Lord Shiva often shown as half-man and half-woman?

 This is the form of Ardhanarishvara (lit. the half-female God)

Shri Ardhanarishvara

I will illustrate the divine symbolism of this form (some are my own interpretations and some are from Shastras).

• It represents the inseperable principle of divine feminine and divine masculine as stated by Hrudaya P .
• From a Yogic perspective, it represents the two prominent Nādis, Ida and Pingala which unite at the Ajna Chakra (commonly called the third eye chakra).
• From a social perspective, it gives us the message to treat the third gender people with utmost respect.

Shri Matre Namah 🙏🏾

Har Har Mahadev 🔱