Should a descriptive biography be written in the third or first person and why?

It depends on the writer. If it is an autobiography, I would say it should be written in first person, if it is a biography written by one person about another person, I would say it should be written in third person.
But I don’t really like the word ‘should’.

I’ve never heard of a biography (account of someone else’s life) that was written in the first person. That would be to present it as if it were an autobiography (account of one’s own life), which is kind of deceptive unless you have a very good reason to do so. It brings it closer to the realm of fiction, then.

If one is writing a descriptive biography of one’s self, it also depends on what it is being written for. A third person description of one’s self could be a creative way of taking a long critical look inward, but would be creepy if it was for a college application or a job interview.

Either one. In fact, if you have trouble writing it in first person, change it to third. Or vice versa. You may find you like it better and find it easier to write one way than the other.