atha cainaḿ nitya-jātaḿ
nityaḿ vā manyase mṛtam
tathāpi tvaḿ mahā-bāho
nainaḿ śocitum arhasi

Translation of Bhagavad Gita 2.26

If, however, you think that the soul [or the symptoms of life] is always born and dies forever, you still have no reason to lament, O mighty-armed.

Commentary by Sri A.C. Bhaktivedanta Swami Prabhupada of Gaudiya Sampradaya:

There is always a class of philosophers, almost akin to the Buddhists, who do not believe in the separate existence of the soul beyond the body. When Lord Krishna spoke the Bhagavad-gita, it appears that such philosophers existed, and they were known as the lokayatikas and vaibhasikas. Such philosophers maintain that life symptoms take place at a certain mature condition of material combination. The modern material scientist and materialist philosophers also think similarly. According to them, the body is a combination of physical elements, and at a certain stage the life symptoms develop by interaction of the physical and chemical elements. The science of anthropology is based on this philosophy. Currently, many pseudo religions—now becoming fashionable in America—are also adhering to this philosophy, as well as to the nihilistic nondevotional Buddhist sects.

Even if Arjuna did not believe in the existence of the soul—as in the vaibhasika philosophy—there would still have been no cause for lamentation. No one laments the loss of a certain bulk of chemicals and stops discharging his prescribed duty. On the other hand, in modern science and scientific warfare, so many tons of chemicals are wasted for achieving victory over the enemy. According to the vaibhasika philosophy, the so-called soul or atma vanishes along with the deterioration of the body. So, in any case, whether Arjuna accepted the Vedic conclusion that there is an atomic soul or he did not believe in the existence of the soul, he had no reason to lament. According to this theory, since there are so many living entities generating out of matter every moment, and so many of them are being vanquished every moment, there is no need to grieve for such incidents. If there were no rebirth for the soul, Arjuna had no reason to be afraid of being affected by sinful reactions due to his killing his grandfather and teacher. But at the same time, Krishna sarcastically addressed Arjuna as maha-bahu, mighty-armed, because He, at least, did not accept the theory of the vaibhasikas, which leaves aside the Vedic wisdom. As a kshatriya, Arjuna belonged to the Vedic culture, and it behooved him to continue to follow its principles.Commentary by Sri Vishvanatha Chakravarthi Thakur of Gaudiya Sampradaya:

“I have presented to you the conclusive truth according to the scripture. Now I will present the truth according to material vision. Please understand it.” Then he speaks this verse.

If you think that the soul is always born (nitya jatam) when the body is born, and always dies (nityam mrtam) with the death of the body, you should not lament for it. O mighty-armed Arjuna, being a brave ksatriya, this war is your dharma.

As Bhagavatam says:

ksatriyanam ayam dharmah prajapati-vinirmitah bhratapi bhrataram hanyad yena ghoratamas tatah

The code of sacred duty for warriors established by Lord Brahma enjoins that one may have to kill even his own brother. That indeed is the most dreadful law.” SB 10.54.40Commentary by Sri Ramanuja of Sri Sampradaya:

2.26 Besides, if you consider this self as identical with the body, which is constantly born and constantly dies — which is nothing other than these characteristics of the body mentioned above —, even then it does not become you to feel grief; because, birth and death are inevitable for the body, whose nature is modification.
Commentary by Sri Sridhara Swami of Rudra Sampradaya:

Thus it has been stated by authoritative testimony that because the soul is neither subject to birth or death there is no need to lament. Now it is being stated that even if one erroneously believes that the eternal soul is perpetually born when the body is born and perpetually dies with the death of the body then and still there is no need for lamentation. Since both virtue and sin with their resultant reactions of birth and death are also attached to the soul perpetually there is still no need to lament.
Commentary by Sri Madhvacharya of Brahma Sampradaya:

Even though the immortal soul is eternal, because of its constant connection and disconnection with the physical body from time immemorial it believes it is experiencing birth and death.

Now begins the summation.

Thus exists this expansive samsara known as the endless cycle of birth and death in the material existence. Until and unless the living entity has attained liberation from the material existence, one is subject to the stringent laws of endless births and deaths in different physical bodies as ordained by the material nature and so are following natural order. Therefore by possessing even this small amount of knowledge there is no need to worry.

In the Shabda Nirnaya it is stated:

Eternal and permanent the immortal soul is known to be and also the immortal soul is eternally in accordance with the cosmic order.

Understanding in the knowledge that there is a cosmic order to existence one should not grieve.
Commentary by Sri Keshava Kashmiri of Kumara Sampradaya:

In this way after establishing the eternal reality of the souls immortality according to the authority of Vedic scripture, the Supreme Lord Krishna describes that it is not intelligent to lament about it, even if one accepts the hypothesis of the Digambaras who believe that the soul is the same size as the body and is born and experiences death along with the body. This is referred to by the particle atha meaning if however, indicating according to another view. Accepting even this other view that the soul is constantly being born and constantly dying there is still no reason to lament about it and the reason why Lord Krishna reveals in the next verse.
Commentary by Sri Adi Shankaracharya of Advaita Sampradaya:

2.26 This (verse), ‘On the other hand,’ etc., is uttered assuming that the Self is transient. Atha ca, on the other hand, if (– conveys the sense of assumption –); following ordinary experience, manyase, you think; enam, this One, the Self under discussion; is nityajatam, born continually, becomes born with the birth of each of the numerous bodies; va, or; nityam, constantly; mrtam, dies, along with the death of each of these (bodies); tatha api, even then, even if the Self be of that nature; tvam, you; maha-baho, O mighty-armed one; na arhasi, ought not; socitum, to grieve; evam, thus, since that which is subject to birth will die, and that which is subject to death will be born; these two are inevitable.
Commentary by Sri Abhinavagupta of Kaula Tantra Sampradaya:    

2.26 Atha va etc. On the other hand if you deam ‘This’ to be the body and to be born constantly,-because its stream does not stop-even then, there is no necessity to lament. Or, if, following the [Vainasika Buddhists’ ?] doctrine of continuous decay of things, you deem This to be constantly dying, even then where is the need for lamenting ? If you, in the same manner, deem the Self to be constantly born or to be constantly dying on account of Its contacts and separations with bodies, even then it is unwarranted, on every account, on the part of the men of rational thinking, to lament. Otherwise this [division of] permanence and impermanence does not stand reasoning. For-
Sanskrit Shloka Without Transliteration Marks:

atha cainam nitya-jatam
nityam va manyase mrtam
tathapi tvam maha-baho
nainam socitum arhasi
Sanskrit to English Word for Word Meanings:

atha — if, however; ca — also; enam — this soul; nitya-jātam — always born; nityam — forever; vā — either; manyase — you so think; mṛtam — dead; tathā api — still; tvam — you; mahā-bāho — O mighty-armed one; na — never; enam — about the soul; śocitum — to lament; arhasi — deserve.