The soul is eternal

Speaking about the nature of the soul, the Transcendental Lord (bhagavān) Śrī Krishna says:

na tv evāhaḿ jātu nāsaḿ na tvaḿ neme janādhipāḥ
na caiva na bhaviṣyāmaḥ sarve vayam ataḥ param

Certainly there was never a time - eva na tu jātu
in which I did not exist; -aham na āsam
Neither you nor all these kings. Even after - na tvam paramna ime jana-adhipāḥ ca
this (war) certainly all these will not cease to exist - na ataḥ sarve vayam eva na bhaviṣyāmah.

Here Śrī Krishna is speaking to Arjuna on the battlefield of Kurukshetra,
refers to the soul and shows its eternal nature.

Eternal means that it is neither born nor dies,
which is clearly the curse imposed by the Christians,
manipulated by Emperor Justinian at the Council of 553.

By the curse, all who believe in the pre-existence of the soul, (implying that it is eternal) were
cursed by them ... See Ban of reincarnation in christianity .

The Supreme Personality Śrī Krishna says in Bhagavad-ghita 2.16-17:

nāsato vidyate bhāvo nābhāvo vidyate sataḥ
ubhayor api dṛṣṭo 'ntas tv anayos tattva-darśibhiḥ
avināśi tu tad viddhi yena sarvam idaḿ tatam
vināśam avyayasyāsya na kaścit kartum arhati

Those who see the truth have concluded - tattva-darśibhiḥ antaḥ.
by seeing both (the material body and soul)- api ubhayor dṛṣṭah
that what is not spiritual (the material body) does not really exist- asatah na vidyate bhāvo
and for that which is spiritual (the soul), there is no non-existence (i.e., it is eternal) - sataḥ na vidyate abhāvah

And know that what pervades this whole (body) (i.e., the soul) is indestructible - tu viddhi tat tatam yena sarvam idam avināśi.
No one is able to destroy that which is indestructible. - na kaścit kartum arhati vināśam asya avyayasya

Bhagavad-ghita 2.19-20:

ya enaṁ vetti hantāraṁ yaś cainaṁ manyate hatam
ubhau tau na vijānīto nāyaṁ hanti na hanyate
na jāyate mriyate vā kadācin nāyaṁ bhūtvā bhavitā vā na bhūyaḥ
ajo nityaḥ śāśvato 'yaṁ purāṇo na hanyate hanyamāne śarīre.

The one who thinks that he is the murderer - yaḥ manyate hantāram
and the one who (thinks that he is) being killed - yaḥ hanyate
both have no transcendental knowledge. - ubhau na vijānītaḥ

For know that it (the soul) - as vetti enam
neither kills nor is killed - na hanti na hatam.

For this (the soul) there is neither birth nor death - ayam na jāyate mriyate vā
there was no time when "it became", nor when "it becomes" or "will become". - kadācit na bhūtvā bhavitā vā na bhūyaḥ

(The soul) is unborn, eternal and unchanging- ajaḥ nityaḥ śāśvataḥ
That original (entity) (the soul) is not killed when the body is killed- ayam purāṇaḥ na hanyate hanyamāne śarīre.