Try cooking something really good that will blow him away - that will prove it :)
I have never cooked my whole life. Now my boyfriend's ALWAYS saying something. I don't really care to do it but even when I tell him I will do it he don't trust me to do it. How can I make him stop saying stuff about it?
Prove to him that you DO know how to cook..nothing too easy tho.
First of all cook something really nice for him! And as you told you haven't cooked your whole life then just start with the next basic thing because if he truly loves you he will surely love what you have made and will appreciate it heartily! And I think you should learn cooking, it's a lot of fun and even your boyfriend will love you more after eating so many delicious things made by you!