Are all homomorphic encryption schemes not CCA secure?
By definition, homomorphic encryption cannot be CCA secure. Therefore when using homomorphic encryption, care must be taken to prevent chosen-ciphertext attacks in the constructed system. Sometimes this requires proving in zero knowledge that certain actions were followed correctly, for example.

If you want to learn a bit more about what can be said about the CCA security of homomorphic encryption, see this paper (On CCA-Secure Somewhat Homomorphic Encryption).