These belligerent senses characterise the modern use of this word, and they have been around since early medieval times. But just as old is a second set of senses, where people challenge in order to demand something as a right - "call for, insist upon". There is no problem with the first sense, which is routine in Shakespeare whenever one person wants to fight another.
It is the second which can cause a problem. When in Henry VI Part 3 (IV.vii.23) Edward says "I challenge nothing but my dukedom", he is demanding to have it, not wanting to fight against it. And when in Richard II (II.iii.133) Bolingbroke says "I am a subject,And I challenge law" he does not mean he is going to break the law; he is simply demanding his rights.
David Crystal is author, with Ben Crystal, of Shakespeare's Words, published by Penguin