Everybody is different in terms of how much exposure it takes before allergy symptoms show up. So in your case, if half a banana is ok but a whole banana is not, then your tolerance threshold is somewhere in between one half and 1 whole banana. This tolerance threshold can be thought of as the top of a barrel. Exposure to one or two allergens (or a few bites of banana) only fills the barrel part-way so no symptoms appear. But exposure to many allergens (or a whole banana) causes the barrel to become so full that it over-flows, and then you get symptoms. Allergies can get worse with continued exposure, meaning the tolerance threshold decreases and thus symptoms appear with smaller and smaller amounts of the allergen. Perhaps seeing an Allergist would give your parents a chance to ask questions and understand more about allergies, thus taking the pressure to eat bananas off of you.
Chronic Lyme Disease, Gluten & Sulfite Sensitivity, Many Food/Inhalant/Medication Allergies & Intolerances, Asthma, Gut issues (dysmotility, non-specific inflammation), UCTD ("Secondary Lupus-Like Syndrome"), Osteoporosis, Anemia, Lymphopenia, intermittant Pancytopenia, chronic malabsorption/malnutrition, etc.; Currently TPN-dependent.
Meds: Zofran, Pulmicort, Vitamin B12 Shots, Heparin (to flush PICC line).