How does asymmetric encryption provide confidentiality?

Asymmetric encryption can provide confidentiality in two ways:

1) messages encrypted using the public key of the recipient can only be decrypted using the private key of the recipient - which only the recipient should possess.

2) It can be used as part of a negotiation process between two users to establish a temporary shared key through a process such as the following:

• User A sends a challenge message to user B which is encrypted with user B's public key to initiate secure communications.
• User B decrypts the message and sends the correct response back to user A encrypted with user A's public key
• The two users are now authenticated to each other
• At this point A can send a proposed symmetric key to B encrypted with B's private key
• All further communications are encrypted via the shared symmetric key

In this second scenario, the asymmetric encryption only facilitates the establishment of confidentiality via the eventually shared symmetric key by securing the initial negotiations.