Radical subjectivity is the claim of one's being-a-subject while rejecting one's attributes and predicates. To refuse to be a subject, on the other hand, is to refuse authority.
The word 'subject' has the related meanings of being the subject of power (sovereign/subject), the subject of study or experimentation (scientist/subject, doctor/subject), and in philosophy just another word for being, ego, consciousness.
This last meaning is a particularly insidious logic of domination, because philosophers are implicitly making the assertion that individuals' being-under-power or being-under-microscopes is inherent to our being.
The radical philosophers then go on speak of radical subjectivity after starting from this premise. Then we can only speak of radical refusals of the attributes upon which power acts, but we have taken our subjectivity for granted, when in fact being a subject is not an essence of being at all.
We do not want to be subjects since to be a subject is to be under. The etymology: "Middle English (in the sense [(person) owing obedience]): from Old French suget, from Latin subjectus ‘brought under,’ past participle of subicere, from sub- ‘under’ + jacere ‘throw.’ Senses relating to philosophy, logic, and grammar are derived ultimately from Aristotle's use of to hupokeimenon meaning [material from which things are made] and [subject of attributes and predicates.]"
Yes, the refusal of attributes and predicates is radical. But the refusal of being subject to attributes, predicates, sovereignty and study is anarchist.