(condensed from Ein Ayah, Shabbat 1:37)

Gemara: Rav Yehoshua the son of Rav Idi came to Rav Ashi’s home. They prepared for him the third calf of its mother (a choice type of meat). They said to him: "Will our master please eat?" He told them that he was in the midst of a fast day. They said to him: "Do you not accept that which Rav Yehuda said: "A person can ‘borrow’ the fast [he accepted upon himself] and ‘pay it back’ [a different day]."

Ein Ayah: There is a rule about mitzvot and obligations of the Torah, especially in matters between man and Hashem. They are supposed to have a desired impact not only in general but even on every individual to make him close to Hashem and bring him to holy actions, characteristics, and viewpoints. On the other hand, a person’s life has to continue normally, without the Torah making overly taxing moral demands on him, as the Rambam (Moreh Nevuchim 3:6) says regarding the Torah acting harmoniously with nature.
Although the goal is that the Torah will make the maximum contribution to every individual, the Torah is still addressed to the community as a whole and its needs. It is forbidden for the individual to "break through the fences" and change limitations and times, even if according to a person’s specific level and situation it would have been better for him had the mitzva been in a different manner or time. This is because the individual has no right to demand that his particular spiritual needs be addressed in the face of unchanging details of the ways of the Torah.
On the other hand, there are opportunities for individual service of Hashem, such as accepting vows and becoming a nazir, through which an individual can construct certain unique added guidelines for himself that are in consonance with his personal needs. There are a variety of related forms that such an approach of accepting additional practices that fit one’s approach of sanctity and piety can take. One of them is a ta’anit yachid (fast of the individual).
Since its whole purpose is to align the personal spiritual needs to correspond to the regular halachot’s appropriateness for the entire community, this sends the message that the standard rules are immutable and cannot be compromised by the individual. To strengthen this message, it is proper that the parameters of such additions of the individual be as flexible to the changing needs of the individual as can be. In that way, the individual can be especially spiritually served while not harming the rules made for the entire community [by equating one with the other].
For that reason, when one has accepted a standard ta’anit yachid, it is possible to "borrow and pay back" if the original day does not presently coincide with his spiritual or even his physical needs. That is indeed in line with the distinction – the community’s obligations are set and unchanging; the special additions for the individual are flexible and fluid.