Answer: Swamiji’s personality is like a vast ocean, unfathomable and illimitable. If we take his words only in parts, we are bound to miss the true purport. So it is advisable and desirable for us to go through his works comprehensively, coupled with deep thinking.
The answer for the question you have asked partly lies in the two lines just before the very sentences of the passage you have quoted. Therein Swamiji has said: “Only the knowers of Brahman are the spiritual teachers of mankind. This is corroborated by all scriptures and by reason too. It is only the selfish…”
Hence it is evident that Swamiji does not refer to Guru-Parampara. Instead Kula-Guru-Paddhati, the system of hereditary gurus is what is being decried. Elsewhere, Swamiji himself has assertively spoken of the necessity of a Guru-Parampara. For instance,
i) Without an unbroken chain of discipleship – Guru-Parampara – nothing can be done… Nothing, I say, can be done without the chain of discipleship, i.e., the power that is transmitted from the Guru to the disciple and from him to his disciple, and so on. (Ref. CW: VI-265)
ii) A Sadguru is one on whom the spiritual power has descended by Guru-Parampara, or an unbroken chain of discipleship. Ref. CW:V-322 (April 2001 edition)
Now, firstly, we need to mark that Kula-guru-paddhati and Guru-Parampara are poles apart. In Kula-Guru-Paddhati there is no question of competency or eligibility. The son of the former priest becomes the successive Kula-guru. Heredity is the only criteria in Kula-Guru-Paddhati. Whereas, Guru-Parampara means an unbroken chain of Brahmajnanis who have realised their own Infinite Divine Nature.
Secondly, when Swamiji said “Hence it is that even through their spiritual practice men do not succeed in perfecting themselves or in realizing Brahman”, here also he refers to the Brahmin teachers who are selfish. For, true Brahmins, i.e., Brahmins in spirit belong to a different category. They are enlightened souls.
Atri-Smriti says :

Janmanaa jaayate shudrah samskaaraat dwija uchyate |

Vedapaathi bhaved vipro brahma jaanaati braahmanah ||

It means “By birth a man is born a Shudra, an ignorant man; through purificatory rites he becomes a dwija, the twice-born; through study and knowledge of the scriptures he becomes a vipra, a scholar or a poet; through the realization of the Supreme Spirit he becomes a Brahmana, a knower of Brahman”.
Hence, we see that when Swamiji speaks about the system of hereditary gurus, he does not mean the genuine teacher-disciple tradition. All scriptures and reason too corroborate it, says Swamiji. Yes, we find such references in Kathopanishad, Mundakopanishad, Svetasvataropanishad, etc.
Swami Vivekananda does not speak against Guru Parampara as such. Spiritual practice without yearning or longing to reach the highest goal and without real spiritual experience or insight will result in only mechanical method which could hardly bring illumination. In Bengal province there was the Kulaguru system about which he refuses there. .