Why can’t DSA be used for encryption?
DSA stands for "Digital Signature Algorithm" - and is specifically designed to produce digital signatures, not perform encryption.

The requirement for public/private keys in this system is for a slightly different purpose - whereas in RSA, a key is needed so anyone can encrypt, in DSA a key is needed so anyone can verify. In RSA, the private key allows decryption; in DSA, the private key allows signature creation.

The fact that RSA also can be used for signatures is a result of the textbook algorithm being a trapdoor permutation - in simple terms, this means the ciphertext and the plaintext are part of the same set space. It is not a requirement of a public key algorithm for this to be the case - public key algorithms just require trapdoor functions.