I even came across people saying "I have fat" instead of "I am fat" because it should not define you.

People, you cannot break grammar to create some affirmation to yourself. Like I am not defined by being pale and I tend to tan in summer, but I don't say "I have pale". I don't say "I have tallness" or "I have 30something".

There are commonly used phrases and sometimes it is about grammar and what sounds right, instead of some silly meaning you add to it and nobody else is able to comprehend.