That's exactly right: it is not a person and therefor does not have rights. That is not circular.
(A) Only persons have rights
(B) A 10 week fetus is not yet a person
Given both (A) and (B) we can conclude (C), that the 10 week old fetus does not have rights.
What is the fallacy you find in that? I do not conclude that the fetus is not a person because it has no rights. That would indeed be circular. I conclude that the fetus is not a person pretty much by looking at it, if you must know.
be·ing /ˈbiɪŋ/ Pronunciation Key - Show Spelled Pronunciation[bee-ing] Pronunciation Key - Show IPA Pronunciation
–noun
1. the fact of existing; existence (as opposed to nonexistence).
2. conscious, mortal existence; life: Our being is as an instantaneous flash of light in the midst of eternal night.
3. substance or nature: of such a being as to arouse fear.
4. something that exists: inanimate beings.
5.
a living thing: strange, exotic beings that live in the depths of the sea.
6. a human being; person: the most beautiful being you could imagine.
7. (initial capital letter) God.
8. Philosophy. a. that which has actuality either materially or in idea.
b. absolute existence in a complete or perfect state, lacking no essential characteristic; essence.
per·son /ˈpɜrsən/ Pronunciation Key - Show Spelled Pronunciation[pur-suhn] Pronunciation Key - Show IPA Pronunciation
–noun
1. a human being, whether man, woman, or child: The table seats four persons.
2.
a human being as distinguished from an animal or a thing.
3. Sociology. an individual human being, esp. with reference to his or her social relationships and behavioral patterns as conditioned by the culture.
4. Philosophy. a self-conscious or rational being.
5. the actual self or individual personality of a human being: You ought not to generalize, but to consider the person you are dealing with.
6. the body of a living human being, sometimes including the clothes being worn: He had no money on his person.
7. the body in its external aspect: an attractive person to look at.
8. a character, part, or role, as in a play or story.
9. an individual of distinction or importance.
10. a person not entitled to social recognition or respect.
11. Law. a human being (natural person) or a group of human beings, a corporation, a partnership, an estate, or other legal entity (artificial person or juristic person) recognized by law as having rights and duties.
12. Grammar. a category found in many languages that is used to distinguish between the speaker of an utterance and those to or about whom he or she is speaking. In English there are three persons in the pronouns, the first represented by I and we, the second by you, and the third by he, she, it, and they. Most verbs have distinct third person singular forms in the present tense, as writes; the verb be has, in addition, a first person singular form am.
13. Theology. any of the three hypostases or modes of being in the Trinity, namely the Father, the Son, and the Holy Ghost.
—Idioms14. be one's own person, to be free from restrictions, control, or dictatorial influence: Now that she's working, she feels that she's her own person.
15. in person, in one's own bodily presence; personally: Applicants are requested to apply in person.
--------------------------------------------------------------------------------
[Origin: 1175–1225; ME persone < L persōna role (in life, a play, or a tale) (LL: member of the Trinity), orig. actor's mask < Etruscan phersu (< Gk prósōpa face, mask) + -na a suffix]
Hmmm.... by the actual definitions of the word... the child is Human, is a "being" and is thus a "person"..... you lose....