I advise you to do some reading up on antigens
, foreign (to the body) proteins or polysaccharides which indeed are a major cause of allergic reactions including asthma - unfortunately, many of which get spread by pets and plants.
Nobody 'blames' these pets and plants for that, it's just a nasty biochemical reaction that takes place in the bodies of allergic people.
Be happy you're not allergic yourself.
Being a huge cat lover, I'd love to have cats myself, but unfortunately my allergic constitution doesn't allow for that.