Can the Buddha ever be a woman? Is it true that the Buddha will never be a woman? If so, why is this?

To be specific, I am particularly asking whether or not the Buddha itself can be female. I am not asking whether a woman can become a Buddha in her future life.
In the (translated into English) Pali text that I have, there's a section titled "The Admission of Women to the Order" within a chapter titled "Stability of Societies". This section describes Ananda's asking the Buddha whether Maha-Pajapati could join the order.

When Ananda asks for the third time, he asks,


  "Lord, are women capable, after going forth from the home unto the homeless life under the Norm-Discipline set forth by the Tathagata, -- are they capable of realizing the Fruit of Stream-winning, of Once-returning, of Never-returning, of Arahantship?


And the Buddha's reply to that question,


  "Women are capable ... of doing so, Ananda."


(Which is why and how Ananda persuaded the Buddha to allow women to be ordained.)



FYI I did a Google search for Bahudhātuka Sutta -- because that seems to be the one/only basis on which other answers claim that a woman's being a Buddha is impossible.

The first search result is this paper, The Bahudhātuka-sutta and its Parallels 
On Women’s Inabilities.

The Abstract for this paper says,


  The present article offers a comparative study of the 
  Bahudhātuka-sutta, based on a translation of one of its parallels 
  found in the Madhyama-āgama preserved in Chinese translation. 
  The study focuses in particular on the dictum that a woman cannot
   be a Buddha, which is absent from the Madhyama-āgama version.


Its conclusions is (page 166),


  the inability of a woman to be a Buddha can still be seen as an expression of leadership conceptions held in ancient Indian patriarchal society


and (page 166)


  This tendency can safely be assumed to stand in contrast to the original teachings of early Buddhism, where -- as far as the texts allow us to judge -- gender was not considered to have an impact on spiritual abilities.


and (page 185)


  Kajiyama (58) concludes that, regarding the listing of inabilities of 
  women, “it is most likely that the dictum did not exist when the Buddhist
  Order maintained one and the same tradition, but that it was created 
  after the Order was divided into many schools and was inserted into 
  sūtras of various schools.” However, the suggestion by Kajiyama (70) that
  “the dictum that a woman is incapable of becoming a Buddha arose 
  probably in the first century B.C.” may be putting things at too late a 
  time. 


The arguments for why is this is a late addition start in the section titled Comparison of the Parallel Versions of the Bahudhātuka Bahudhātuka-sutta on page 151 and can be summarized as:


Evidence that other parts were added:


"Aggregates" seems to be new
Items were added to the "elements" topic


Therefore it's possible that an item (the item regarding women) was added to the "impossibilities" section.
The difference between versions could be explained as a later addition (into some versions), or as a later loss (from the other versions); but an addition is more likely.
There are various other differences in the "impossibilities" section.
The "impossibilities for women" doesn't exist in all versions
In the versions which do include the "impossibilities for women" section, there are differences between versions.
Buddha's being a woman, or low-caste, would be incompatible with contemporary society (because they wouldn't be respected when alive), which was the reason for the argument that a woman would have to be reborn as a man before she could be the Buddha
Some versions (not the Pali) say that a woman cannot even be a Paccekabuddha, which is proof that more and more degradation of women's abilities were added over time. (page 164)
It's therefore significant that one of the versions doesn't mention it at all (i.e. it implies that it wasn't original)
The addition doesn't fit, wasn't useful in the context of other information which was intended to be practical (page 166)




Maybe could better link the transition of the context? (from arahantship being possible to women, to the question at hand)

I think you're asking why my first quote (the Buddha's reply to Ananda's question, which was about "Arahantship") is relevant to this question, which is about the Buddha.

The paper I linked to above says that, at that time, no-one had the ambition of becoming the future Buddha: perhaps Arahant was synonymous with the highest feasible spiritual attainment, and that women were able no less than men to achieve it (page 163):


  Here it needs also to be taken into account that the presentation 
  in the Bahudhātuka-sutta and its parallels still stems from a period in the 
  development of Buddhist thought when the idea of aspiring to Buddhahood
   had not yet become a general option. As pointed out by Kajiyama 
  (64), “the dictum that a woman cannot become a Buddha ... did not have 
  a target to which it could have been directed,” since at that time “no
  one, neither man nor woman, aspired to Buddhahood.”53 In sum, then, 
  the inability of a woman to assume the position of a ruler on earth, a ruler
  in various heavenly realms, or a ruler in the field of Dharma reflects 
  leadership conceptions in ancient India. 


The footnote says,


  53 Romberg (164) notes that once “the aim was no longer to become an 
  Arhat, but to become Buddha ... this shift made, in fact, the situation for 
  women worse, because a doctrinal foundation was laid for the necessity 
  of changing the sex before being able to become enlightened.” In fact the 
  Bodhisattvabhūmi explains that a woman will not realize the awakening of 
  a Buddha because already an advanced bodhisattva has left behind womanhood
  for good and will not be reborn again as a female, Wogihara 
  (94,3): na ca strī anuttarāṃ samyaksaṃbodhim abhisaṃbudhyate. tat kasya 
  hetoḥ? tathā hi bodhisattvaḥ prathamasyaiva kalpāsaṃkhyeyasyātyayāt strībhāvaṃ vijahāti bodhimaṇḍaniṣadanam upādāya na punar jātu strī bhavati; cf. 
  also Paul (212 note 7). Harrison (78) concludes that “women ... are generally represented in such an unfavourable light as to vitiate any notion of 
  the Mahāyāna as a movement for sexual equality. Compared with the 
  situation in the Pāli Canon, in which women are at least as capable as
  men of attaining the highest goal, arhatship, the position of women in 
  Mahāyāna has hardly changed for the better.”