Halfway Up the Flagpole With No Way Down

There's a thing you're never supposed to do when you fight with your kids, and that's to capitulate halfway through a battle. 

But sometimes you pick a certain battle and exactly halfway through, you realize that it isn't worth it--that the battle you picked was a stupid one, and the thing your child is demanding really isn't that unreasonable. 

But you can't give in now! Because giving in now will reward a tantrum. And you can't reward a tantrum! So you're at an impasse. You're halfway up the flagpole with no way down.

Here's an example of what I mean. I call this particular battle "Bath v. Shower" and it went like this:

Me: Paige, go take a shower.
Paige: No, I want to take a bath.
Me: No, it's almost bedtime and a shower will be faster.
Paige: I promise it'll be really fast.
Me: No, you need to take a shower. You'll also get cleaner.
Paige: No I won't! I'll get really clean. I promise!
Me: PAIGE!! I said take a shower. So get in the shower!
Paige: BUT I WANT TO TAKE A BAAAAATTTTHH! NOT A SHOWERRRRRRRRRRRR!!
Me (Silently): Why am I fighting over this? If I'd just said yes to a bath the first time she would have LITERALLY been out of the bath already. 
Me (Aloud): TAKE A SHOWER!!!
Paige: NOOOOOOOOOO!!!!!!!!
Me: (Silently): This was such a stupid fight. Why did I pick it? Why do I care if she takes a bath or a shower? How do I get out of this now though? If I say yes now after this whole meltdown it sends a bad message. She'll think all she has to do is push hard enough and she'll get her way every time. It's the principle of the thing.
Me: (Aloud): Forget it. We're not taking either one. 
Paige: Fine by me.
Me (Silently): FUUUUUUUCK!! Check-mated again! 

And another silent question I ask myself all the time: How am I still so bad at this?!

The kids and me, a year or two ago during my peak poor battle-picking.