Look let me sum up Putin's argument for you guys (and I'll try not to be a little cocksucker about it like he is) and let me know if you think any differently at all.
krellin et al., do a google image search on Buck Angel (NSFW). Do you find this person attractive? I'll assume you do not. Why not? You identify as heterosexual, this person is a woman by sex. Isn't it then fair to say that heterosexual isn't actually the BEST descriptor for your feelings? Though it's by and large an accurate term for most situations, if you're like me you find femininity in general more important than merely the sex of the person. Putin has proposed the word "gynephilic" to accurately represent this.
Now, you and I, we don't really care, right? 99.9% of the time, a person we are attracted to affirms both our gynephilic and our heterosexual identities.
But what if we were transgendered and preferred masculinity to femininity? The term "homosexual" doesn't even really apply to us. Sure, we have penises, and sure we may even tend to date people who also have penises, but the term homosexual is fairly misleading, isn't it? It casts confusion on not only our gender identity but then by default on the gender identity we prefer (since homo means same, but people are confused as to what we are, then they will ask, "same as what?")
In this case, the reasons for the superiority of a word like "androphilic" become apparent. There is no confusion as to what we find attractive, it is defined in the word itself, rather than requiring the context of one's own sex (which may not be immediately apparent) to convey meaning.
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So all in all, do I think the word homosexual is offensive? No. But I do accept that it is an inferior descriptor compared to the terms Putin has proposed. the "philics" encompass all of the meaning that terms like hetero- and homo-sexual offer. The only thing that gets lost by switching is whether a person prefers their own biological sex or not, which we've already established with the Buck Angel example is fairly meaningless.
Hopefully that sums it up.