Why was Lord Buddha reluctant to ordain females as Bhikkuni initially?

Buddha generally advised training for calm.

The theme of sexuality is something associated with a lot of strong emotion and one genereally needs some sort of rehabilitative conditioning to manage impulses.

AN 1.1 This is how I heard. At one time the Buddha was staying in the city of Sāvatthī in Jeta’s park, at Anāthapiṇḍika’s monastery. There, the Buddha addressed the monks, “Monks!”

“Bhante,” they replied. The Buddha said this: “Monks, I do not see a single sight that obsesses a man’s mind like the sight of a woman. The sight of a woman obsesses a man’s mind.”

AN 1.2 “Monks, I do not see a single sound that obsesses a man’s mind like the sound of a woman. The sound of a woman obsesses a man’s mind.”

AN 1.3 “Monks, I do not see a single smell that obsesses a man’s mind like the smell of a woman. The smell of a woman obsesses a man’s mind.”

AN 1.4 “Monks, I do not see a single taste that obsesses a man’s mind like the taste of a woman. The taste of a woman obsesses a man’s mind.”

AN 1.5 “Monks, I do not see a single touch that obsesses a man’s mind like the touch of a woman. The touch of a woman obsesses a man’s mind.”

AN 1.6 “Monks, I do not see a single sight that obsesses a woman’s mind like the sight of a man. The sight of a man obsesses a woman’s mind.”

AN 1.7 “Monks, I do not see a single sound that obsesses a woman’s mind like the sound of a man. The sound of a man obsesses a woman’s mind.”

AN 1.8 “Monks, I do not see a single smell that obsesses a woman’s mind like the smell of a man. The smell of a man obsesses a woman’s mind.”

AN 1.9 “Monks, I do not see a single taste that obsesses a woman’s mind like the taste of a man. The taste of a man obsesses a woman’s mind.”

AN 1.10 “Monks, I do not see a single touch that obsesses a woman’s mind like the touch of a man. The touch of a man obsesses a woman’s mind.”

DN 16 23. Then the Venerable Ananda said to the Blessed One: "How, Lord, should we conduct ourselves towards women?"

"Do not see them, Ananda."

"But, Lord, if we do see them?"

"Do not speak, Ananda."

"But, Lord, if they should speak to us?"

"Then, Ananda, you should establish mindfulness."

[1] "There is the case of the monk who, on seeing a cloud of dust, falters, faints, doesn't steel himself, can't continue in the holy life. Declaring his weakness in the training, he leaves the training and returns to the lower life. What is the cloud of dust for him? There is the case of the monk who hears, 'In that village or town over there is a woman or girl who is shapely, good-looking, charming, endowed with the foremost lotus-like complexion.' On hearing this, he falters, faints, doesn't steel himself, can't continue in the holy life. Declaring his weakness in the training, he leaves the training and returns to the lower life. That, for him, is the cloud of dust. This individual, I tell you, is like the warrior who, on seeing a cloud of dust, falters, faints, doesn't steel himself, can't engage in the battle. Some individuals are like this. This is the first type of warrior-like individual who can be found existing among the monks.

[2] "Then there is the case of the monk who can handle the cloud of dust, but on seeing the top of the enemy's banner, he falters, faints, doesn't steel himself, can't continue in the holy life. Declaring his weakness in the training, he leaves the training and returns to the lower life. What is the top of the banner for him? There is the case of the monk who not only hears that 'In that village or town over there is a woman or girl who is shapely, good-looking, charming, endowed with the foremost lotus-like complexion.' He sees for himself that in that village or town over there is a woman or girl who is shapely, good-looking, charming, endowed with the foremost lotus-like complexion. On seeing her, he falters, faints, doesn't steel himself, can't continue in the holy life. Declaring his weakness in the training, he leaves the training and returns to the lower life. That, for him, is the top of the banner. This individual, I tell you, is like the warrior who can handle the cloud of dust, but on seeing the top of the enemy's banner, he falters, faints, doesn't steel himself, can't engage in the battle. Some individuals are like this. This is the second type of warrior-like individual who can be found existing among the monks.

[3] "Then there is the case of the monk who can handle the cloud of dust & the top of the enemy's banner, but on hearing the tumult [of the approaching forces], he falters, faints, doesn't steel himself, can't continue in the holy life. Declaring his weakness in the training, he leaves the training and returns to the lower life. What is the tumult for him? There is the case of the monk who has gone to the wilderness, to the foot of a tree, or to an empty building. A woman approaches him and giggles at him, calls out to him, laughs aloud, & teases him. On being giggled at, called out to, laughed at, & teased by the woman, he falters, faints, doesn't steel himself, can't continue in the holy life. Declaring his weakness in the training, he leaves the training and returns to the lower life. That, for him, is the tumult. This individual, I tell you, is like the warrior who can handle the cloud of dust & the top of the enemy's banner, but on hearing the tumult he falters, faints, doesn't steel himself, can't engage in the battle. Some individuals are like this. This is the third type of warrior-like individual who can be found existing among the monks.

[4] "Then there is the case of the monk who can handle the cloud of dust, the top of the enemy's banner, & the tumult, but when in hand-to-hand combat he is struck and falls wounded. What is the hand-to-hand combat for him? There is the case of the monk who has gone to the wilderness, to the foot of a tree, or to an empty building. A woman approaches him and sits down right next to him, lies down right next to him, throws herself all over him. When she sits down right next to him, lies down right next to him, and throws herself all over him, he — without renouncing the training, without declaring his weakness — engages in sexual intercourse. This, for him, is hand-to-hand combat. This individual, I tell you, is like the warrior who can handle the cloud of dust, the top of the enemy's banner, & the tumult, but when in hand-to-hand combat he is struck and falls wounded. Some individuals are like this. This is the fourth type of warrior-like individual who can be found existing among the monks.

[5] "Then there is the case of the monk who can handle the cloud of dust, the top of the enemy's banner, the tumult, & hand-to-hand combat. On winning the battle, victorious in battle, he comes out at the very head of the battle. What is victory in the battle for him? There is the case of the monk who has gone to the wilderness, to the foot of a tree, or to an empty dwelling. A woman approaches him and sits down right next to him, lies down right next to him, throws herself all over him. When she sits down right next to him, lies down right next to him, and throws herself all over him, he extricates himself, frees himself, and goes off where he will.

"He resorts to a secluded dwelling place: the wilderness, the foot of a tree, a mountain, a glen, a hillside cave, a charnel ground, a forest grove, the open air, a haystack. Having gone to the wilderness, the foot of a tree, or an empty building, he sits down, crosses his legs, holds his body erect, and brings mindfulness to the fore. - an5.75

This is like taking a reactive dog away from what is distracting, to retrain it properly in a calm environment where it can be rehabilitated to act & think adequately.

Buddha wasn't categorically pro gender segregation because it is also said that women can be Arahants and one should follow a wise person and take a companion who is one's equal or better.

I think it makes sense that allowing women to establish their Sangha nearby reeks trouble for the upholding of brahmacariya among the bhikkhus and that is only compensated by a likewise compromised bhikkhuni sangha.

Instead of have one strong sangha which is lower in number, one recruits a larger group but the whole is then inherently compromised and the upright traditions won't be upheld as long as could've been if the bhikkhus were secluded.

“But, Ānanda, if women had not obtained the Going-forth from the home life into homelessness in the Dhamma & Vinaya made known by the Tathāgata, the holy life would have lasted long, the true Dhamma would have lasted 1,000 years. But now that they have obtained the Going-forth from the home life into homelessness in the Dhamma & Vinaya made known by the Tathāgata, the holy life will not last long, the true Dhamma will last only 500 years.

“Just as a clan in which there are many women and few men is easily plundered by robbers and thieves, in the same way, in whatever Dhamma & Vinaya women obtain the Going-forth from home life into homelessness, the holy life does not last long.

“Just as, when the white blight falls on a field of ripening wheat, that field of wheat does not last long, in the same way, in whatever Dhamma & Vinaya women obtain the Going-forth from home life into homelessness, the holy life does not last long.

“Just as, when the rust disease falls on a field of sugar cane, that field of sugar cane does not last long, in the same way, in whatever Dhamma & Vinaya women obtain the Going-forth from home life into homelessness, the holy life does not last long.

“Just as a man might make an embankment in advance around a great reservoir to keep the waters from overflowing, in the same way I have set forth in advance the eight rules of respect for nuns that they are not to transgress as long as they live.” - an8.51

As to the validity of this particular story, i think it is generally true because it makes sense and is complete with excellent analogies.

The stock phrase in the suttas is a man leaves the household life for freedom, as follows:

He [the person discussed above], hearing the Dhamma, gains conviction in the Tathāgata and reflects: 'Household life is confining, a dusty path. Life gone forth is the open air. It isn't easy, living at home, to practice the holy life totally perfect, totally pure, a polished shell. What if I, having shaved off my hair & beard and putting on the ochre robe, were to go forth from the household life into homelessness?'

Mahatanhasankhaya Sutta

Therefore the monks, at times, lived in forests and caves and roamed around northern India at will. We can also read in the suttas some well-practised monks travelled in India to spread the Teachings and were murdered by hostile opposition.

When women joined the Sangha, obviously they had to be protected. Unlike men who are disposable assets, such as conscripted as soldiers in war, society does not generally accept endangering the lives of women. If the daughters of good families became nuns and were often raped or murdered, the Buddha's Sangha would obviously fall into disrepute.

Therefore, to ordain women was obviously a loss of freedom for the monks, in that the Sangha would somewhat resemble the household life, where monks would be involved in the protection of nuns. To a bhikkhu (monk), such as activity can be disgusting.

If you look at the actual story in question, Mahapajapati wasn't asking the Buddha to ordain women in general, but was only asking about herself, and the Buddha was reluctant. I should note that some modern scholarship seems to suggest that this story could be fabricated.

Even if the story is true, the reasons for his reluctance couldn't have been because he didn't want there to be a Bhikkhuni order, because the Vinaya has a section that describes Mara trying to convince the Buddha to pass into Parinibbana, and the Buddha kept giving reasons not to, and once he said that he wouldn't because he hadn't established the Bhikkhuni order yet, so it seems that the Buddha intended to have an order of Bhikkhunis from the beginning.

there's an alternative point of view suggesting that if the Mahapajapati's story is indeed authentic, it postdates the first acceptance of a woman into the Sangha, who could be Bhadda Kundalakesa, and that reluctance of the Buddha concerns specific circumstances of that particular episode and not wholesale refusal of women entrance into the order

Bhadda Kundalakesa Therigatha (Thig 5.9)

I traveled before in a single cloth,
With shaven head, covered in dust,
Thinking of faults in the faultless,
While in the faulty seeing no faults.
When done was the day's abiding,
I went to Mount Vulture Peak
And saw the stainless Buddha
By the Order of Bhikkhus revered.
Then before Him my hands in añjali
Humbly, I bowed down on my knees.
"Come, Bhadda," He said to me:
And thus was I ordained.
Debt-free, I traveled for fifty years
In Anga, Magadha and Vajji,
In Kasi and Kosala, too,
Living on the alms of the land.
That lay-supporter — wise man indeed —
May many merits accrue to him!
Who gave a robe to Bhadda for
Free of all ties is she.

the issue is dealt with at length in the Ven Sujato's book "White Bones Red Rot Black Snakes" (free)

the history behind the issue appears very misty to me, where the truth probably won't ever be found out