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In symmetric key cryptography, the same key is used by both parties Sender use this key and encryption algorithm to encrypt message and the receiver use same key and corresponding decryption algorithm to decrypt it .
In symmetric key cryptography the same key is used for encryption and decryption purpose so the key is shared between sender and receiver due to this Symmetric key cryptography also known as shared secret key cryptography.

In asymmetric key cryptography sender has two keys public key and private key similarly Receiver has two key public key and private key.
In short there are four keys used for communication between sender and receiver.
If Sender use his public key for encryption then receiver was unable to decrypt the message because message will be decrypted only by sender's private key that is only known by sender not receiver.
If sender use his private key for encryption then for decryption receiver require sender's public key that is public for all user who connected via network then anyone can decrypt the message and confidentiality of message does not remain so that this way is not valid .
If sender use receiver's private key for encryption then it is impossible receiver's private key is only known by receiver not sender so that this way is not valid.
If sender use receiver's public key for encryption and it is possible because receiver's public key is public for all users who connected via network so sender can easily encrypt message via receiver's public key Receiver decrypt the message using his own private key and here confidentiality of data remain because no one else receiver decrypt the message because receiver's private key is only known by receiver not anyone else.
So,
In asymmetric key cryptography (also known as public key cryptography) receiver's public key is used for encryption by sender and receiver use his or her private key to decrypt the message.

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