Just a hunch, but is your little guy pretty smart and stubborn?
If so, he's playing you like a fiddle, mama. Two year olds are notorious control freaks, it's just how they're built. Add in a mommy who begs him to eat and puts an endless parade of food in front of him, complete with swirly spoon and airplane noises... well, it's every toddler's dream! What's not to love?
Your doctor isn't lying to you. If he's hungry, he'll eat. Just put a plate in front of him that contains whatever the rest of the family is eating. If he eats it, great! If he doesn't, oh well. Don't make any commentary, don't threaten or bribe or beg. If he doesn't eat, just clear his plate from the table along with everyone else's and move on with your day. He can eat at the next meal/snack time if he so chooses, but not until then.
As an aside, my younger child has always been tiny for her age and eats about a tablespoon of food at a time (she's almost 5 and is 32 pounds!). I was very worried at first but then realized I was making a big issue of something that didn't require it. Now she has to sit at the table with the rest of us, but if she doesn't eat, I really don't care. She is healthy and active and bright, and that's all that matters. Kids are actually really good at knowing how much food they need.
No worries, mama. Just keep feeding him at regular meal times, and eventually he'll eat.