How is it possible to be very allergic to dogs but not cats?

I have no problem with cats but with dogs is a different story. If a friend or relative have a dog in the house, I start sneezing, eyes start itching and coughing a lot. Days later I start developing rashes on my face, neck and arms and parts of my legs.

I went to an allergist specialist. It came out negative on cats but positive (the area got red and swollen so fast) on dogs. How is that possible? To be very allergic to dogs but not cats?

How is it possible to be very allergic to dogs but not cats?
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