In my opinion, this is a "No true Scotsman" fallacy. You are claiming that someone who develops an allergy must have had an allergy to start with. But the only

In my opinion, this is a "No true Scotsman" fallacy. You are claiming that someone who develops an allergy must have had an allergy to start with. But the only thing that backs up this claim is your own definition. I would suggest that allergy ought instead to have a clinical definition: if you can observe symptoms, you have an allergy. This definition is the only one that makes practical sense: if you could not observe symptoms, why would you care? The immune response definition that you give does not match up well with what medical professionals would call allergies - not at all. It's clear that repeated exposure can cause an allergy in this sense, and you have presented no valid argument to debunk that.