The rationales

Executions don't happen at anyone's whim. Even wrongful executions in the USA (certainly not the same in every death penalty country) happen after a formal procedure of arrest, indictment, trial, verdict and sentencing. Not even the staunchest pro-abortionist can honestly deny that abortion happens on a whim; they just think that that whim shouldn't be illegal.

Military deaths happen to people who are also armed and can shoot back. At least in theory - it is true that the US armed forces aren't too bright at preventing non-combatant deaths; but no army in the world can honestly claim that it can fight a war without killing any non-combatant, at that. In any case, the intention in war is to shoot the combatants who can also shoot back, not just anyone they want. And I've never heard of an armed fetus, not even in Texas...

I also know that public opinion in Canada, Britain and Western Europe is strongly against death penalty. But you have to understand that most Americans (albeit not all, and widely varying across regional and other social lines...) agree with death penalty. You also have to understand that "agree with death penalty" will in itself vary very much - as to what crimes, on what burden of proof, by what method of execution, and so on...