While it is true, of course, that abortion is infanticide, there may be situations in which it is confusing to use that word.  Sometimes one might wish to make a distinction between murdering children before birth and doing so after birth.  

For example, if one were describing the progression of the error, one might say that the social acceptance of abortion led to the acceptance of infanticide.  Obviously, it is unclear to say "the acceptance of infanticide led to the acceptance of infanticide".   So we sometimes need terminology capable of showing this distinction.

I agree that "pro-choice" is a problematic word for various reasons and ought to be avoided.  What we replace it with would depend on the context.  I think that, while "pro-abortion" has some negative points, there are circuмstances in which it is acceptable.

Abortion is infanticide as you confirmed in the first sentence. From there on everything you wrote is an attempt to soften that fact when speaking to the world. That defeats the entire purpose. The use of euphemisms like abortion, pro-choice etc. is not reality.

I do not see the word "abortion" as a euphemism.  It comes from the Latin word abortio and is used in medical terminology.  A "spontaneous abortion" is commonly called a miscarriage, while an "induced abortion" is commonly called an abortion and means the deliberate killing of a child before birth.  It is a precise and clinical word that does not soften the reality of what occurs.

You are correct, it is not a euphemism strictly speaking, but it has become like one, since the term is used to mean many mechanical operations like "aborting a mission". 

Yes, this is what I was getting at by saying that using "pro-choice" to refer to support for abortion is deceptive.  One could more rightly call the Catholic position "pro-choice" since it is based on the correct understanding of free will.