I find this fascinating. As an artist myself, I am very surprised by the amount of anger that comes from that. Is it so bad for someone to be so amazed by your art that they wish they had your skill? And to be fair, no, not everyone can do art, even with a lot of practice. My only thought is be mindful of the person as well. Why take a compliment so offensively? I have many people I aspire my art to be like, and my art is not to their level, nor will it be. Try to remember the motive behind such words and do not be so quick to criticize. Perhaps that is where the world would find itself a better place.
Consider taking the compliment graciously and for what it is, a compliment. And then redirect the attention of the complimenter, offer them resources to help them learn and say "Well these are some things I did to get this good, and you can do them too." How much farther can we all get if we chose that over bashing people for a compliment, or even a lack of self confidence.