Actually, something rather like homeopathy's ridiculous dilution does work for some food allergies. You start by taking a tiny bit of whatever it is you're allergic to. Then you take a tiny bit more. It's called oral immunotherapy.
Oral Immunotherapy and Homeopathy are nothing alike.
Why? Because as you say the former involves taking a "tiny bit" of something that you are allergic to and slowly increasing the amount and thus "training" your immune system.
Homeopathy on the other hand requires you to dilute the substance to such a degree that all is left is solvent (water, alcohol, etc.). There is none of the original material that is being dissolved left!
In other words. Your "tiny bit" of food is an absolutely massive amount in comparison to no food at all and even if the homeopath decides to not dilute to the point to which they claim to do a "tiny bit" of food will probably amount to a few grams vs the femtograms left over after a series of dilutions.