The question and answer quoted in the article is in the book Mani Ratna Mala
which is said to be the work of Shree Adi Shankaracharya. Translated by by Paramhans, Swami Yoganand. Shloka no. 3
This book is in the question and answers , asked by Shishya and answers given by Guru.
This is the whole verse.
संसार ह्रुत्कस्तु निजात्म बोध : |
को मोक्ष हेतु: प्रथित: स एव
द्वारं किमेक नरकस्य नारी |
का सर्वदा प्राणभृतामहींसा ।।3।।
Samsara Hrutkastu Nijatma Bodha
Ko Moksha Hetuhu Prathitaha sa
Dwaram Kimekam Narasya Nari
Ka Sarvada PranaBhrutaMahimsa
Shishya - Who takes us beyond Sansara ?
Guru - The realisation
of self takes one beyond samsara and the person then gets detached
from Samsara. i.e. Atma Bodha.
Shishya - What is the Root Cause of Moksha?
Guru- The famous
Atma Bodha OR self realisation is.
Shishya - What is the gate to hell.?
Guru - Women is gate of hell.
Shishya - What facilities us with moksha?
Guru - Ahimsa
Before answering your question let us see in what context the word "Women" is used and why in Hinduism scriptures.
We at many places find such similar verses portraying women as gate to hell or an obstacle etc. It appears though our scriptures are demeaning women. But in reality often the word Women isn't used for actual women , but for "Maya of the Lord in the form of women"
For example this verse of Shreemad Bhagvat Purana is also saying "Women are gate to hell"
सङ्गं न कुर्यात्प्रमदासु जातु
योगस्य पारं परमारुरुक्षुः ।
वदन्ति या निरयद्वारमस्य ॥39॥
sańgaḿ na kuryāt pramadāsu jātu
yogasya pāraḿ param
One who aspires to reach the culmination of yoga and has realized his
self by rendering service unto Me should never associate with an
attractive woman, for such a woman is declared in the scripture to be
the gateway to hell for the advancing devotee.SB 3.31.39
But if we look at the next verse , there it's said that Women are created by Lord is the representation of his Maya.
योपयाति शनैर्माया योषिद्देवविनिर्मिता ।
तृणैः कूपमिवावृतम् ॥40॥
yopayāti śanair māyā
tṛṇaiḥ kūpam ivāvṛtam
The woman, created by the Lord, is the representation of maya, and one who associates with such maya by accepting services must certainly
know that this is the way of death, just like a blind well covered
with grass.SB 3.31.40
So the word women is often used as Maya , and women does not necessarily mean a physical women but a representation of worldy pleasures. That simply mean an advice not to indulge / attach in women (Maya) too much.
So in conclusion we can say that what Shree Adi Shankaracharya mean by "Women is gate to hell" is this maya of the Lord in the form of women is one of the gate of hell.
And may be he is not pointing towards women directly but using / giving an example of obstacles for those who are going in the path of Moksha, mainly sanyasis to keep away from material pleasures.
This is clear by this shloka of Mundaka Upanishad ,On which Shree Adi-Shankara written commentary. As the main objective of the verse no.3 from Mani Ratna Mala is retirement from sanyasa , atmabodha and to show the powerfullness of sexual desire. as given in index.
नायमात्मा बलहीनेन लभ्यो न च प्रमादात्तपसो वाप्यलिङ्गात् ।
एतैरुपायैर्यतते यस्तु विद्वांस्तस्यैष आत्मा विशते ब्रह्मधाम ॥
nāyamātmā balahīnena labhyo na ca
vidvāṃstasyaiṣa ātmā viśate
brahmadhāma || 3.2.4 ||
4 This Atman cannot he attained by one devoid of strength or by excitement or by tapas devoid of linga. But of the knower who strives
with these aids, the Atman enters into the Brahman.
Shankar Bhashys -because this Atman cannot be attained by one devoid of strength produced by concentration on the Atman or by excitement caused by associating with objects of the world, as son, cattle and the rest, or by tapas devoid of linga. ‘Tapas’ here means ‘knowledge.’ “Linga,” means “Sanyasa.” The meaning is that the Atman cannot be attained by knowledge without Sanyasa.
Note - Below Shloka of shloka 3 of Mani Ratna Mala book the detail explanation of the answers given by guru is provided by the translator.
And the translator is giving ref.of puranas to explain his point. hence I have used ref.from puranas.