When someone doesn't like a certain thing about your character, character being yourself, like maybe they don't like the way you explain things as an example or simply that they don't like that you lie or whatever. It could even be physical, like they don't like your nose or something.
undesirable: not wanted or desirable because harmful, objectionable, or unpleasant.
characteristic: typical of a particular person, place, or thing or a feature or quality belonging typically to a person, place, or thing and serving to identify them.
It could even be like refferring to a physical object or building, like "ohh this grandiose manor has a few undesirable characteristics like that naked person over there, couldn't possibly live in a house with nudists!"
Usually it's just what people with a stick up their arse talk like to say they don't like something.
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The term Aspergers is no longer officially used in the UK - it is now regarded as High Functioning Autism.