Just say that it is a very friendly species, very safe, and it will be kept in his habitat. Later when things cool down, you can take it out just to see it. Don't bring up crickets just say mealworms that are kept in a secure can. My mother freaks out about crickets because they smell and chirp and there jumpy.
Ask them why, specifically, they don't want to let you have one. If you have done enough research, you should be able to recommended a comprimise. But, sometimes parents don't need a reason to say no. If they still won't agree, drop it. You might just have to wait until you move out.