Actually the matter is simple the hadith appears in a Chapter entitled "Breastfeeding an adult" and the sentence before quoting this hadith says:
المقصود بالرضاعة هنا أن تفرغ المرأة لبنها في إناء وترسله للرجل ليشربه وتكرر ذلك خمس مرات وبذلك تحرم عليه.
My own translation take it carefully!
What is meant by suckling here is that a woman may pour her breast milk into a vessel and send it to the man to drink it and repeat this procedure five times so that she becomes a mahram.
This is well known as procedure which has been mostly narrated on the authority of 'Aishah. See also Sunan ibn Majah & suckling.
I actually don't know anybody else than ibn Hazm who said that suckling happened or was necessary for the case of breast feeding an adult. Only al-Albani -among contemporary scholars- agreed to this. And scholars already discussed this earlier.
This hadith actually appears almost all hadith collections except with Sahih al-Bukhari, here a quote from a longer version from al-Muwatta':
"Sahla bint Suhayl who was the wife of Abu Hudhayfa, and one of the tribe of Amr ibn Luayy, came to the Messenger of Allah, may Allah bless him and grant him peace, and said, 'Messenger of Allah! We think of Salim as a son and he comes in to see me while I am uncovered. We only have one room, so what do you think about the situation?' The Messenger of Allah, may Allah bless him and grant him peace, said, 'Give him five drinks of your milk and he will be mahram by it.' She then saw him as a foster son. A'isha umm al-muminin took that as a precedent for whatever men she wanted to be able to come to see her. She ordered her sister, Umm Kulthum bint Abi Bakr as-Siddiq and the daughters of her brother to give milk to whichever men she wanted to be able to come in to see her. The rest of the wives of the Prophet, may Allah bless him and grant him peace, refused to let anyone come in to them by such nursing. They said, 'No! By Allah! We think that what the Messenger of Allah, may Allah bless him and grant him peace, ordered Sahla bint Suhayl to do was only an indulgence concerning the nursing of Salim alone. No! By Allah! No one will come in upon us by such nursing!'
"This is what the wives of the Prophet, may Allah bless him and grant him peace, thought about the suckling of an older person."
So this narration makes clear that the other wives of the prophet () had a different opinion on the matter. And this is the view of the majority too so this could be another reason why ibn abi Mulaikiah didn't narrate this.
Az-Zurqani in his commentary on al-Muwatta' added a narration actually explaining how Sahla gave milk to Salim:
وكأن القائلين بأن ظاهر الحديث أنه رضع من ثديها لم يقفوا على شيء . فقد روى ابن سعد عن الواقدي عن محمد بن عبد الله بن أخي الزهري عن أبيه قال : كانت سهلة تحلب في إناء قدر رضعته ، فيشربه سالم في كل يوم ، حتى مضت خمسة أيام ، فكان بعد ذلك يدخل عليها وهي حاسرة ، رخصة من رسول الله صلى الله عليه وسلم لسهلة
My own translation take it with all necessary care.
...As if those who toke the hadith literally and said she gave him his breast have never hear/read anything. As it was narrated by ibn Sa'ad from al_Waqidi from Muhammad ibn 'Abdullah the son of az-Zuhri's brother from his father who said: Sahlah was milking a quantity for his breast feeding (of her milk) in a vessel. Salim drunk this each day until fuive days have passed. Afterwards he (could) enter (her house) while she was bareheaded (unveiled), as a permission from the Messenger of Allah Allah's prayers and blessings be upon him to Shalah.
As for the part:
I refrained from (narrating this hadith) for a year or so on account of fear. I then met al-Qasim and said to him: You narrated to me a hadith which I did not narrate (to anyone) afterwards.
Scholars interpret it as a respect or maybe "fearful respect", as he asked al-Qassim again to get his authorization to narrate the hadith, because on one side the involved people were alive and on the other side the majority of sahabah and the mothers of believers rejected the idea of breast feeding an adult to gain mahram relationship (as is stated in the reference proposed by @UmH).
And this goes ahead with an-Nasa-i's narration of the hadith:
It was narrated that 'Aishah said:
"Sahlah came to the Messenger of Allah and said: 'O Messenger of Allah, Salim enters upon us and he understands what men understand, and knows what men know.' He said: 'Breast-feed him, and you will become unlawful to him thereby.'
(Ibn Abi Mulaikah, one of the narrators said:) For a year I did not narrate this, then I met Al-Qasim and he said: 'Narrate it and do not worry about it.'" (Sunan an-Nasa-i)
See also this Article in Arabic showing more details and discussing what somebody concluded from al-Albani's statement.