First, they say that sexual orientation discrimination is "analogous" to sex discrimination:

INFRINGEMENT OF ARTICLE 15 - WHETHER 'SEXUAL ORIENTATION' IS A GROUND ANALOGOUS TO 'SEX'

99. Article 15 is an instance and particular application of the right of equality which is generally stated in Article 14. Article 14 is genus while Article 15 along with Article 16 are
species although all of them occupy same field and the doctrine of "equality" embodied in these Articles has many facets. Article 15 prohibits discrimination on several enumerated grounds, which include 'sex'. The argument of the petitioner is that 'sex' in Article 15(1) must be read expansively to include a prohibition of discrimination on the ground of sexual orientation as the prohibited ground of sexdiscrimination cannot be read as applying to gender simpliciter. The purpose underlying the fundamental right against sex discrimination is to prevent behaviour that treats people differently for reason of not being in conformity with generalization concerning "normal" or "natural" gender roles. Discrimination on the basis of sexual orientation is itself grounded in stereotypical judgments and generalization about the conduct of either sex. This is stated to be the legal position in International Law and comparative jurisprudence. Reliance was placed on judgments of Human Rights Committee and also on the judgments of Canadian
and South African courts.

100. International Covenant on Civil and Political Rights (ICCPR) recognises the right to equality and states that, "the law shall prohibit any discrimination on any ground such as race, colour, sex, language, religion, political or other opinion, national or social region, property, birth or other status". In Toonen v. Australia (supra), the Human Rights Committee, while holding that certain provisions of the Tasmanian Criminal Code which criminalise various forms of sexual conduct between men violated the ICCPR, observed that the reference to 'sex' in Article 2, paragraphs 1 and 26 (of the ICCPR) is to be taken as including 'sexual orientation'. [The decision cites long blocks of Canadian and South African case law here.]

104. We hold that sexual orientation is a ground analogous to sex and that discrimination on the basis of sexual orientation is not permitted by Article 15. Further, Article 15(2) incorporates the notion of horizontal application of rights. In other words, it even prohibits discrimination of one citizen by another in matters of access to public spaces. In our view, discrimination on the ground of sexual orientation is impermissible even on the horizontal application of the right enshrined under Article 15.

And the Court found that they "moral indignation" isn't reason enough to discriminate:

The argument of the learned ASG that public morality of homosexual conduct might open floodgates of delinquent behaviour is not founded upon any substantive material, even from such jurisdictions where sodomy laws have been abolished. Insofar as basis of this argument is concerned, as pointed out by Wolfenden Committee, it is often no more than the expression of revulsion against what is regarded as unnatural, sinful or disgusting. Moral indignation, howsoever strong, is not a valid basis for overriding individuals's fundamental rights of dignity and privacy.In our scheme of things, constitutional morality must outweigh the argument of public morality, even if it be the majoritarian view. In Indian context, the latest report (172nd) of Law Commission on the subject instead shows heightened realisation about urgent need to follow global trends on the issue of sexual offences. In fact, the admitted case of Union of India that Section 377 IPC has generally been used in cases of sexual abuse or child abuse, and conversely that it has hardly ever been used in cases of consenting adults, shows that criminalisation of adult same- sex conduct does not serve any public interest. The compelling state interest rather demands that public health measures are strengthened by de-criminalisation of such activity, so that they can be identified and better focused upon.

For the above reasons we are unable to accept the stand of the Union of India that there is a need for retention of Section 377 IPC to cover consensual sexual acts between adults in private on the ground of public morality.

And a great conclusion:

The notion of equality in the Indian Constitution flows from the 'Objective Resolution' moved by Pandit Jawaharlal Nehru on December 13, 1946. Nehru, in his speech, moving this Resolution wished that the House should consider the Resolution not in a spirit of narrow legal wording, but rather look at the spirit behind that Resolution. He said, "Words are magic things often enough, but even the magic of words sometimes cannot convey the magic of the human spirit and of a Nation's passion........ (The Resolution) seeks very feebly to tell the world of what we have thought or dreamt of so long, and what we now hope to achieve in the near future." [Constituent Assembly Debates: Lok Sabha
Secretariat, New Delhi: 1999, Vol. I, pages 57-65]. 130. If there is one constitutional tenet that can be said to be underlying theme of the Indian Constitution, it is that of 'inclusiveness'. This Court believes that Indian Constitution reflects this value deeply ingrained in Indian society, nurtured over several generations. The inclusiveness that Indian society traditionally displayed, literally in every aspect of life, is manifest in recognising a role in society for everyone. Those perceived by the majority as "deviants' or 'different' are not on that score excluded or ostracised.

131. Where society can display inclusiveness and understanding, such persons can be assured of a life of dignity and nondiscrimination. This was the 'spirit behind the Resolution' of which Nehru spoke so passionately. In our view, Indian
Constitutional law does not permit the statutory criminal law to be held captive by the popular misconceptions of who the LGBTs are. It cannot be forgotten that discrimination is antithesis of equality and that it is the recognition of equality which will foster the dignity of every individual.

132. We declare that Section 377 IPC, insofar it criminalises consensual sexual acts of adults in private, is violative of Articles 21, 14 and 15 of the Constitution. The provisions of Section 377 IPC will continue to govern non-consensual penile non-vaginal sex and penile non-vaginal sex involving minors. By 'adult' we mean everyone who is 18 years of age and above. A person below 18 would be presumed not to be able to consent to a sexual act. This clarification will hold till, of course, Parliament chooses to amend the law to effectuate the recommendation of the Law Commission of India in its 172nd Report which we believe removes a great deal of confusion. Secondly, we clarify that our judgment will not result in the re-opening of criminal cases involving Section 377 IPC that have already attained finality.

We allow the writ petition in the above terms.

Overall, it's a passionate defense of the right to live and let live, of the need for laws to serve a positive purpose in order to be upheld, and of the basic democratic tenet that the minority cannot be trampled on by the majority. Indian LGBT people have a big reason to celebrate today.