My orthodontist claims that my overbite could never be corrected due to the thickness of my teeth? Is this true? (Photo)

I've had an issue with my overbite and two front teeth sticking out and having a very large appearance. I've had braces for about 14 months now. My ortho gave me the option of tooth extraction AFTER just braces and wearing elastics if I'm not satisfied. But 5 months in treatment, he tells me removing teeth will take 5-6 years to NEVER correcting my bite due to my teeth being "thick". Are there any other options? Is my Ortho lying to me because he doesn't want to remove teeth and he's lazy?