Why use symmetric encryption in a protocol like UPORT? Reading the whitepaper
UPORT: A PLATFORM FOR SELF-SOVEREIGN IDENTITY ~ DRAFT VERSION (2016-10-20)
I noticed it states :

Let A be an attestation. Suppose we wish to share this attestation with only identities X, Y and Z. We first generate a random symmetric key k, and encrypt A symmetrically. We denote this ciphertext sym(k, A).
Now we assume that X, Y and Z each have a public encryption key. Let asym(U,V,d) denote the asymmetric encryption between identities U and V of some data d. Specifically asym(U,V,d) = sym(DH(U,V),d)
Where DH(U,V) is a symmetric key generated from the public key of U and the private key of V using a Diffie-Hellman key exchange.
Create a random and ephemeral public/private key pair R, and create the data blob made up of ( sym(k,A), asym(X,R,k), asym(Y,R,k), asym(Z,R,k) )

Why is A encrypted symmetrically?
Reading the Security.SE questions “Why is symmetric encryption still used? [duplicate]” and “Asymmetric vs Symmetric Encryption” a potential reason for using symmetric encryption is speed but I don't see the context reasoning for using it in this specific case?
It's multi-layered encryption. If you "layer" your encryption you gain quite some nice flexibility features which is what they have done here.

You have some secret ($A$) which you only wish to share with parties $X,Y,Z$ for which you also know the public key. So what you do is that you first pick a random public-private-keypair $R$ yourself and derive a new shared secret with each of them. Now you have three shared secrets which would mean you'd have to encrypt three different copies of your message $A$. Instead you only encrypt a key $k$ three times using the shared secrets (using DLIES) and then in turn use $k$ to grant access (by means of symmetric encryption) to $A$. This approach saves you quite a bit of bandwidth and computational power there as you only need to encrypt a large message once instead of three times.

In a graphic, this process would look like this (don't forget that $k$ is small and $A$ is potentially large):