Since I kind of grew up with the conviction that my misery didn't matter, a conviction that I've never been able to really shake, I have a different way of answering this:
I have two children. (Okay, they're in their 20's, but only chronologically.) What do they need? Some miserable, depressed parent who is likely to die soon because he can't look forward to anything except being dead? A parent who preaches honesty but is all too obviously living a lie?
The claim that you're harming your children by transitioning is, pardon my French, BS. Your kids may not like it, but then, they probably don't like having to go to school or cleaning up their room, either. In the long run, though, they need an honest parent, one who can give of their entire self, rather than a fraud. (And what kind of example does that set them, if you and your wife in effect run away when faced with something tough?)
And that's the point. People who insist you should deny your TG nature are asking you to participate in a lie, a mutual lie to spare them a momentary bit of inconvenience. It's like painting over dry rot -- in the long run, the lie will spread and ruin everything until the whole structure collapses. Better in the long run to dig out and remove the dry rot (the lie) as soon as you see it.
I mean, if you'd broken your leg, going on walking around on it would, in the (very!) short run, spare the people around you some hassle, but of course in the long run, it would be a whole lot worse for everyone.
I understand the desire to deny it. If you break your leg, usually the first thought is like, no, this isn't happening, can't I pretend it's just a bad bruise? But you have to address it, and address it promptly, to avoid much bigger problems down the road.