This reminds me of the fate vs freewill debate....
In much of the history of traditional wizardry literature, the wizard is ambivalent when it comes to sexuality (Gandalf, for example). Also, Merlin was essentially asexual (as was his conception) until he became involved with Niniane, and then ended up defunct. The sexual digression was more of a metaphor of his (and his type of magic) leaving the world to the more political, earthy nature that Arthur's Age represented. Sometimes the magician (not necessarily a wizard - perhaps the pinnacle of ethereality possible in human form) will use sexuality as a means to an end, as did Niniane, rather than the enactment of a biological imperative. Somehow, they have chosen to remove themselves from the mammalian and romantic aspect of their natures to serve other purposes, nothing to do with family and personal intimacy.
Dumbledore follows the same archetype. Dumbledore's sexuality seems very much related to his mentality (a magician's trait). That he is attracted to another with strong mentality is no wonder. I think the same-sex interest would not be as strong as an equivalent-mentality interest. If there was a female character in his past with the same mentality, the interest would be there too methinks. That there isn't would make it seem that Dumbledore is only interested in the same sex, as it's likely that he is typical of the wizard's ilk and is generally asexual, though strongly aroused through mental chemistry - and why his love remains unrequited. Dumbledore is attracted to the world of ideas and magic, the not-human that Grindelwald represented most strongly to him. The "***" tag is perhaps only how muggles would make sense of the relationship.