Why can’t DSA be used for encryption? This question at StackOverflow mentions that DSA cannot be used for encryption. But both RSA and DSA can be used to generate public and private keys, right? Then why can't I use the DSA public key to encrypt?
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.