There are verses that say so.

The swan [Brahman] said, ‘I disclose unto you a great mystery. There is no status that is superior to that of humanity. Freed from sin like the Moon from the murky clouds, the man of wisdom, shining in resplendence, attains to success by patiently waiting for his time. A person of restrained soul, who becomes the object of adoration with all by becoming the foremost of the supporting pillars of the universe, and towards whom only agreeable words are spoken by all, attains to the companionship of the deities.’

Mahabharata Santi Parva Section CCC

Number of births and importance of human birth

In the eighty four lacs of bodies of creatures one does not acquire true knowledge anywhere unless one is born as a man.

Here, after thousands of crores of births a creature obtains human form only sometime due to aggregate of virtue.

Having obtained a rare human form he should endeavour for moksha. If he does not endeavour for it, there can be no greater sinner in the world.

Born in the most beautiful human form he incurs the sin of slaying a Brahmin if he neglects his self.

Without human body it is not possible to obtain the supreme goal. One should be, therefore, very cautious to guard wealth in the form of his body and perform good actions.

……

So far as this body remains intact he should practice dharma. One is a perfect fool who digs a well only when the house is on fire.

[Garuda Purana, Dharma Khanda, Chapter XLIX]

Why can humans do it?

The straightforward answer is that the man has the capacity to free himself from sin.

Why can animals not do it?

The reason is man has the necessary intelligence which animals lack.

As long as the body is healthy, free from sickness, as long as old age has not set in, as long as the power of sense-organs is not impaired, as long as there is no risk to life, an intelligent man should endeavour for the welfare of the soul. It is foolishness to dig a well when the house has caught fire.

[Garuda Purana, Dharma Khanda, chapter XIII]

There are verses that say so.

The swan [Brahman] said, ‘I disclose unto you a great mystery. There is no status that is superior to that of humanity. Freed from sin like the Moon from the murky clouds, the man of wisdom, shining in resplendence, attains to success by patiently waiting for his time. A person of restrained soul, who becomes the object of adoration with all by becoming the foremost of the supporting pillars of the universe, and towards whom only agreeable words are spoken by all, attains to the companionship of the deities.’

Mahabharata Santi Parva Section CCC

Number of births and importance of human birth

In the eighty four lacs of bodies of creatures one does not acquire true knowledge anywhere unless one is born as a man.

Here, after thousands of crores of births a creature obtains human form only sometime due to aggregate of virtue.

Having obtained a rare human form he should endeavour for moksha. If he does not endeavour for it, there can be no greater sinner in the world.

Born in the most beautiful human form he incurs the sin of slaying a Brahmin if he neglects his self.

Without human body it is not possible to obtain the supreme goal. One should be, therefore, very cautious to guard wealth in the form of his body and perform good actions.

……

So far as this body remains intact he should practice dharma. One is a perfect fool who digs a well only when the house is on fire.

[Garuda Purana, Dharma Khanda, Chapter XLIX]

Why can humans do it?

The straightforward answer is that the man has the capacity to free himself from sin.

Why can animals not do it?

The reason is man has the necessary intelligence which animals lack.

As long as the body is healthy, free from sickness, as long as old age has not set in, as long as the power of sense-organs is not impaired, as long as there is no risk to life, an intelligent man should endeavour for the welfare of the soul. It is foolishness to dig a well when the house has caught fire.

[Garuda Purana, Dharma Khanda, chapter XIII]