They're against the idea because disorder is a label of negative value. Homosexuality can be studied just fine without labeling it a disorder.
I think it's not science. It commits the fallacy of functionalism, by conflating statistical normality, or how common something is, with a metaphysical judgment of value. Nature can only make mistakes if it's preprogrammed, even if imperfectly, for a particular purpose, and thus can be judged according to the value of its specific developments in serving that purpose. That's an argument with religious origins, even when it's disguised. For example, when someone says "the purpose of life is to reproduce," that is a functionalist fallacy, since it assumes nature is the vessel of some kind of end goal, and then that phenomena that help towards achieving this end are thus inherently good while those that do not are inherently bad. Even having the instinct to reproduce in one's DNA does not and cannot demonstrate that reproduction is a goal in this ultimately religious sense, and thus, cannot be used to judge people who do not want to reproduce as bad in some way. Similarly, the author's distinction between homosexuality and left-handedness is completely unsupported and unsupportable without resorting to this same fallacy.
Life has no demonstrable purpose. It only has tendencies that we can measure and declare stronger or weaker. Thus, homosexuality is a statistical abnormality, or a weaker tendency, since it is not common- but being a statistical abnormality is not an indication of any inherent value or lack thereof. In other words, it's not unnatural. Being the result of uncommon genetic mutations and chemical ratios and life experiences doesn't make it unnatural.
If nature contains no inherent meanings and values, then the only meanings there are come from us. We have decided that something like depression is a disorder, because it impairs the ability of an individual by their own standards (and survival, or living a fulfilling life, or any other standard here, is ultimately man-made, even if it's influenced by instinct.) We have decided that psychosis is a disorder, because it not only impairs the individual, but can cause that individual to harm others around them. Homosexuality does none of these things. Therefore, it makes no sense to label it a disorder.
Studying the origins of all these phenomena are useful for different reasons. Again, labeling homosexuality a disorder automatically leads to social and political problems because it devalues it to the status of something that must be fixed or otherwise eliminated, as with the other things that people label disorders.