Conceptual analysis certainly DOES require necessity. No analysis of units of meaning would ever ignore the impossible, the probable and improbable, the possible, and the certain.
There are several types of necessity according to traditions in philosophy, but the concepts of necessity and contingency are rooted in deeper metaphysical questions, such as what is metaphysical necessity itself? Let's take a look at some of the types of necessity that philosophical analysis relies on broadly.
Logical Necessity
In logical necessity, the emphasis is on the logical operators. In your second example, for instance, you have used exclusive disjunction. It is necessary a sibling is either a brother or a sister but not both. Setting aside the intensions of the words, one might ask if the logical relation you present is accurate. Is your claim true in the face of the possibility a sibling might be born and determined to be intersex? Here, the consequence being examined is the disjunction itself.
Nomic/Nomonological Necessity
According to the SEP's Varieties of Modality, some philosophers hold certain necessities are guaranteed by causal determinism, empirical fact, or laws of the universe, which are necessarily weaker or stronger than metaphysical necessity, depending on the philsoopher. From the article:
We are inclined to say that nothing can move faster than light to express the fact that the laws rule out superluminal motion, and to state Newton’s First Law by saying that an object cannot depart from uniform rectilinear motion unless acted on by an external force. This motivates the thought that there is a form of necessity associated with the natural laws.
Causal Necessity
Also known as (causal) determinism, this is the view that events in time are essentially necessary given prior events. This is classic territory in regards to the nature of the physical universe, Newtonian mechanics, and questions of free-will
Metaphysical Necessity
Given my limited expertise, this is the most contentious of necessities which seems to cover various philosophers views on a bewildering array of claims regarding the analytic-synthetic divide, a prioriticity and a posteriority, universals and particulars, entities and properties, modality and necessity itself, and so on. Here, the giants of philosophy use the term when squaring off about first principles. Here, philosophers seem to invoke broad claims of necessity about philosophical positions or what SEP calls metaphysical grounding. From the article:
Some suggest that this and similar claims are grounding claims, where grounding is understood to be a form of constitutive (as opposed to causal or probabilistic) determination or explanation. The point of departure for theorizing about grounding is that there are a variety of claims—claims we make in ordinary life as well as ones we make in the context of doing philosophy—that are best interpreted as being claims about what grounds what. As for metaphysics in particular, some claim that grounding plays a central role in the enterprise properly conceived. Schaffer, for example, writes that “metaphysics as I understand it is about what grounds what” rather than what exists (2009: 379)
When debating existence, for instance, one often appeals to grounds to prove existence.
Linguistic or Semantic Necessity
This is the one you ask after. In linguistics, the relationship between green and colored is one of hyponomy/hyperonomy. That is, it is necessary that green things are colored, but note that it is not necessary that colored things are green. This is a form semantic necessity because it is derived from the relationship of the intensions of words.
Why Your Second Example Includes Necessity
When you say:
To be green is to be coloured.
You can paraphrase as 'If something is green, then it is coloured' (G->C). When you say:
To be a sibling is to be either a brother or a sister.
Necessity also exists. By paraphrase, 'If one has a sibling, it is either a brother or a sister' (Sib->Bro XOR Sis). In both cases, you are dealing with the conditional, and it is this conditional logical expression that encapsulates necessity. It just so happens that you have exclusive disjunction in the consequent of the second one. The presence of conjunction and disjunction in conditional claims doesn't undo the necessity built into the claim as a whole. Thus, if one has a sibling, it is necessary that one has a sibling (Sib->Sib), and most accurately if one has a sibling, it is necessary that is a brother, sister or an intersex sibling (Sib->Bro XOR Sis XOR Inter) at least in real world cases.
