Verse 2

2)
jantUnAm narajanma durlabham atah pumstvam tato vipratA
tasmad vaidikadharmamArgaparatA vidvatvam asmAt param|
AtmAnAtmavivecanam svanubhavo brahmAtmanA samstitih
muktirno satakotijanmasu krtaih: punyairvinA labhyate||

Of all births, that as a human being is rare to obtain. rarer still is to be born as a male; rarer than that is to be born a BrAhmana. More difficult than that is to be inclined towards the path of dharma declared by the Vedas. Successively more difficult than this are scholarships (in the revealed texts), discrimination between the Atman and anAtman, perfect experience following profound meditation, the state of being established in Brahman and lastly, mukti or liberation. These cannot be obtained without merit acquired in hundreds of crores of lives.

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I am taking the liberty here of abridging HH's comments as it runs to 9 pages!! It is truly amazing how one verse can mean soooo much. Sorry for this abridging, and if it seems incomplete, do let me know and I will copy more of it in later posts.
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Like the verse in the bhagavad Gita: ashocyAnanvashocastvam praj~nAvAdAmsca bhAsase | gatAsUnagatAsUmsca nAnusocanti paNditAh: || "Thou grievest for those who should not be grieved for; thou speakest like wise men; but those who have attained Atmaj~nAna are not concerned either with the state of death or of being alive", this verse in the vivekachUdAmani beginning with jantUnAm ... gives in a nutshell the entire substance of the work.

An Astika alone is qualified to embark on the study of VedAnta sAstra. An Astika is one who believes in the existence of the Atman apart from the body. By saying that birt as a human being is difficult to obtain, the fact of the exixtence of th Atman apart from the body is conveyed by implication. The word jantUnAm means 'jananaSIlAnAm', those who are subject to janana or creation in the world. The difficulty of obtaining sucha a birth can be stated only on the basis that one goes through many births successively. Birth means combination of Atman with a body, and so again, separateness of Atman from the body is implied. It behoves a person to obtain a body which will produce happiness and joy and avoid one that will cause grief. By this is indicated the duty to endeavour towards punya and avoid pApa, which will get a good body and bad body respectively.

 Regarding what is Punya and what is pApa, sAstra is the one which prescribes laws and lays down prohibitions. As an Astika alone believes in the supremacy if the sAstras and hence he alone is qualified for a study of the sAstras. The next thing stated by Sri BhagavatpAda as more difficult to obtain than a mere human body is to be born as a male human being; for women are not qualified to study the vedas. The idea is that they can never know and realsie the Atman which can be done only by a concentrated study of the Upanishads. The reason for such disqualification may be that Veda-adhyayana and VedAntavichara are whole time occupations for which women are unfit by reason of their involvementin domestic duties such aschild baring and child rearing activities.

Next in the list of things rare to obtain is vipratA, being a Brahmana. It is true that although Kshyatriya and vaishyas also are considered twice borns, they have other serious duties like taking care of the kingdoms etc., and these are all inherently outward directing. Moreover, as stated in the Sruti's, Samyasa is essential to realise the Ultimate, and to qualify for sanyasa, one has to ascend to Brahmin hood. It is to be noted here that Sri Bhagavat pAda does not say dvijatva (being twice borns) as being difficult to obtain, but vipratA, i.e, being a BrAhmana. Next, vipratA will itself not help one get Knowledge. Having been born a BrAhmana, one should engage in observance of the prescribed Dharmas. It is important to note here that Sri Shankara says "DharmamArgaprapatA", not "karmamArgaprapatA"; This shows that the supreme objective of man can be secured only by Dharma. It is said, " dharatIti dharmah: dhriyate anena iti vA dharmah:". "Because it supports the world, it is dharma; or it (the Universe) is supported by this, hence it called Dharma". Dharma is super sensous, and cannot be perceived by any of the senses. Men can comprehend it only by using sAstra as authority. hence the emphasis on the word vaidika when saying vaidika dharmamArgaprapatA. It is also to be carefully noted here that Vedas are considered as the ONLY source of the knowledge of Dharma. For when one says "I live by driking water", it is not be understood as "drinking water and also drinking or eating somethiing else". Just so, from the Vedas means from only the vedas.

The karma MImAmsakas hold that dharma by itself is the final means for the attainment of eternal bliss and that there is nothing else that is required. Sri BhagavatpAda indicates his dissent by using the word "mArga" in vaidika dharma mArga prapatA.

The karma MImAmsakas hold that dharma by itself is the final means for the attainment of eternal bliss and that there is nothing else that is required. Sri Bhagavat pAda indicates his dissent from this view by using the word mArga in the expression 'vaidikadharmamArgaprapatA'. This use of the word mArga shows that dharma cannot by itself, directly or immediately, give the bliss of moksha. It is to the same effect that sage bAdarAyana speaks when he says: 

dvAvimAvatha pantAnau yatra vedAh pratisthitAh:| pravrttilakSano dharma nivrttisca prakIrtitah:|| 

"Two are the paths laid down in the Vedas. Dharma is said to be of two kinds, of of the nature of pravrtti (dharma towrds or worldly activity) or of nivrtti (dharma away from or withdrawal from the world)."

(A lot more is quoted by His Holiness in this context. Some from Sri Sankara's GitAbhAsya, some from Sri Sankara's sopAnapa~nchaka and the mahabharata. All these quotes, in one form or another support this same main idea that Dharma and other good vitures alone make a Brahman QUALIFIED for a rigourous study of the Upanishads. It is not sufficient by itself.)

Next in the order of things difficult to obtain as stated by Sri BhagavatpAda in this sloka is vidvatvam. This relates to both kinds of Dharma (quoted above). In relation to pravritti dharma, it refers to the performance of vedic rites with the understanding of the meaning of the mantras uttered to the aacompaniment of the rites. Sri BhagavatpAda has stated several times (elsewhere): It is common knowledge that when a dealer in diamonds and fisherman, each comes by a precious stone, by his knowledge of the nature of the object, the former makes a huge profit which is not the case with the latter.

In respect of nivrttidharmas, vidvatvam means this: It has been said: "samnyasya sravanam kuryAt" which means that one should hear about (receive instruction in and obtain knowledge of) Vedantic texts after taking samnyAsa. So vidvatvam here means mediated knowledge (of Brahman) obtained by listening to the upadesa on vedAntic texts. This is known as parokSajn~ana as distinguished from immediate knowledge of brahman synonymous with its realistation which is called aparokSajn~ana. The next requisite for final liberation is Atma-anAtma vivecanam. This will be explained at length in the course of this work. It means mananam or deep reflection on the distinction of the Atman and the non-Atman. This reflection results in the firm conviction of the truth of the srutis supported by proper reasoning. By constantly meditating on the import of the sruti, one gets rid of all doubts respecting the means to knowledge and the goal of knowledge and one avoids wrong understanding of the meaning.

Then comes svanubhavah. By this is meant direct realisation of brahman preceded by nididhyAsana (constant meditation on the upadesa of the Guru). This understanding is called nididhyAsana. Hence it is called svanubhavah (su- anubhava), proper and perfect anubhava. By this also is converyed the four fold steps for spiritual wisdom, namely: subecchA (the longing for release preceded by vairAgya or detachment), vicArana (listening to and reflection on the upadesa of the guru which takes the form of ascertaining the meaning of the words of the sruti in accord with the criteria for determining their import: tAtparya lingasaha karana vAkyArthanirdhanam sravanam), tanumAnasA (having a light mind unaffected by sense objects), and satvapatti (being mentally established in the Supreme reality or the sadvastu).

That these must be further accompanied by non attachment (asasaktih), the state of absence of awareness of things internal or external (padArthAbhAvanA), and remaining steadfast on one's natural self (turyagA) is indicated by the last term in the series which is brahmAtmanA samsthitih, being firmly established in Brahman, which means liberation. By this is also implied that the states of sAmpIya (being in close proximity to the Supreme), sAlokya (being in the same world), sArUpya (being of the same form) and sAyujya (unitive experience) are not of the nature of liberation in its proper true sense. As they all pertain to the saguna Brahman, these four are to be considered as mithyA or unreal. The Ultimate Brahman is free from the limitations of place, time and objects and such freedom from limitation cannot be predicated of the saguna Brahman. "BrahmAtmanA samsthitih:" means being free from connection with all imagined limitations and remaining in one's true state of fulness as ever pure, intelligent, free and non-different from one's inner self. This is called kaivalyam. this is being alone, free from every taint or upAdhi. This is liberation. This cannot be secured except by merit (punya) acquired by good deeds done in hundreds of crores of lives.