Maybe you ought to actually watch the showing before trashing it? It may very well be what you think and it very well may not.
As for getting upset people think she's him, well, i'd probably be pissed, too, if i was a 5'-6", 110 pound woman being mistaken for a 6'-4" 220 pound guy. You'd also think 24" of bright red hair would be a giveaway as well. It's not like the whole story is out there, we know from the cross over bruce/batman disappeared awhile ago. Don't know why, and i don't think they said how long ago. But, there's been a decided gap. No one was doing the job, she stepped in and it should be readily apparent, she's not him.
I don't know the comic origin, but Batwoman's been a round a good long time. It's not like they just invented her exclusively from the show, in which case, you'd have a point. It'd be up there with making Thor a woman in my book in which case create a new one, don't take the mantle of an old one. But this one did exist, it wasn't just created.
And to be quite honest, they're doing this because DC (the brass) is stupid and won't let them use batman, otherwise, this would likely be batman. Just like smallville, you could have clark, but not superman, which was dumb. Gotham let them use bruce, but not batman. They're not letting WB/Berlanti use batman is likely why the went this route. I actually like the fact that it's an unknown character to me as well, but that's another issue. Their claim is they trying to avoid confusion (BS). Superman does exist in Supergirl and doesn't create confusion with the movies. Flash TV existed years before Flash movie and that wasn't confusion (to them at least). But, batman in both places they believe still causes confusion, let alone in the mind of most viewers of either screen size that they all know Keaton, Kilmer, Clooney, Bale, Affleck, and frankly West all as batman on different screens in basically 4 different universes and they're adding a 5th universe and another actor.
DC is the clueless one here. Berlanti and Co have done a better job with the characters they've been permitted to use than DC has with their current 'universe' on the big screen (except for WW and possible Aquaman (haven't seen that one)).
But please bash something as a fait accompli over 2 minutes of trailer of a show that hasn't finished a handful of episodes yet. It's one thing to think it isn't for you, it's something else to trash it over it's content due to a couple of lines.