As revised, I think this question is really asking why the judge in Grainger plc v Nicholson  UKEAT 0219_09_0311 laid down the test that he did, when the statutory provision at hand used more general words.
In summary, the reason why the Grainger test does not protect every belief is that the European Convention on Human Rights doesn't either. The judge's conclusions on the ECHR's notion of "belief" are mainly taken from the analysis in a House of Lords case (Williamson, cited below), which is binding precedent on the tribunal on that point. The new thing was drawing the line between "belief" in ECHR jurisprudence, and "belief" in the employment equality regulations, which was justified for two reasons: one, that Parliament demonstrably was trying to make the alignment; and two, that it would be incoherent with the Convention obligations to do otherwise.
Note that the definitions in the Equality Act 2010 are carried forward from the 2003 regulations which were at issue in Grainger, the Employment Equality (Religion or Belief) Regulations 2003, so we have to look at this text instead. In 2(1) it said, following amendments in 2006 not shown in the online text:
In these Regulations –
i. "religion" means any religion,
ii. "belief" means any religious or philosophical belief,
iii. a reference to religion includes a reference to lack of religion, and
iv. a reference to belief includes a reference to lack of belief.
This regulation was introduced in order to bring EU Directive 2000/78/EC into UK law. Although the text in the 2010 Act is not identical, it does carry forward the same effect of the Directive, and so the decision still makes sense to apply. Also, Brexit has happened, but that does not displace the reasoning.
In interpreting the provision:
- Because it derives from EU law, which is meant to mean the same thing in other member states, the domestic regulation should be read consistently with the directive. The court can look to EU authorities to find out what the directive ought to mean, although there was not much to look at in this instance.
- The respondent said that "belief" should be read consistently with the language in the European Convention on Human Rights, concerning religion, belief and discrimination - principally Articles 9(1) and 14. The court was still bound to read the domestic legislation in a way that is at least compatible with the Convention rights, even if the scope of "belief" is not absolutely identical (see paragraph 19 of the judgement), but the most obvious way to make the ideas compatible is if they are the same.
- The parliamentary history of the amending statute shows indications that it was made in awareness of ECHR case law about "belief". Courts can sometimes use this kind of information to resolve genuine textual ambiguities.
The judge looked to domestic precedent, in particular a decision of the House of Lords (R (Williamson) v Secretary of State for Education and Employment  UKHL 15) which looked at the same provisions of the ECHR in the context of a claimed philosophical belief in favour of corporal punishment in schools. This in turn drew on extensive case law, including even an English ecclesiastical case from 1866, as well as many more recent sources from around the world. The thrust of all of this is that not every single possible propositional belief is protected by the ECHR; when it talks about belief it does not mean "a statement which somebody somewhere believes to be true", but rather refers to certain kinds of philosophical conviction.
The application of this idea to employment discrimination is new in Grainger, hence "the Grainger test", but wrangling over the scope of "belief" is not new. The test itself, set out in paragraph 24, is really a collation of quotations from the various relevant past judgements. I won't try to figure out the exact provenance of all of the words since that is actually already set out in the judgement. But for example,
(iii) It must be a belief as to a weighty and substantial aspect of human life and behaviour.
comes from paragraph 36 of Campbell and Cosans v UK  4 EHRR 293,
... the applicants' views relate to a weighty and substantial aspect of human life and behaviour ...
(v) It must be worthy of respect in a democratic society, be not incompatible with human dignity and not conflict with the fundamental rights of others
is there because of Article 17 of the ECHR, as interpreted in Campbell (citations omitted in this quotation),
the expression "philosophical convictions" in the present context denotes, in the Court's opinion, such convictions as are worthy of respect in a "democratic society" and are not incompatible with human dignity; in addition, they must not conflict with the fundamental right of the child to education, the whole of Article 2 (P1-2) being dominated by its first sentence
This of course raises the question of why the ECHR's scope is what it is. That is somewhat more of a policy question than a legal one, in that the treaty reflects what its parties felt comfortable with agreeing. What matters in legal terms is that the Convention is binding on the UK, and the words that it uses must be interpreted according to what Convention authority (the Strasbourg court) says that they mean.