Don't think I do, actually. But anyhoo
Do you think that the Church doesn't oppose abortion? Or do you think that the Church doesn't state that its moral teachings are objective? Or is there something you are seeing that I am missing?
The claim that humans are "created in the image of God" is hardly an objective claim, is it?
Serious question: do you even know what the word "objective" means?
It doesn't mean "something agreed upon by everyone." Not everyone agrees that the series implied by the decimal expansion .999999..... converges to 1, but it is objectively true that it does (since the conclusion follows necessarily once the terms "series," "decimal expansion" and "converges" are understood).
One way to define an objective truth is something which is truly independent of any individual. That we are posting on a message board is an objective truth, even if someone were to dispute it. You may object that we may be confused about what is happening and having a hallucination or something, but in that case it would be objectively true that we were not posting on a message board. The truth wouldn't become subjective just because someone (or even everyone) is mistaken about it.
I can't see why you would not think that this statement would be a statement about objective truth. I can see people disagreeing about it certainly, but they would be saying that is objectively false, not that it is subjectively true and false.
Specifics are important. But now that you've identified them, perhaps you'd care to tell me what's so special about a "living human organism"? Remember, we're talking about objective, here, that can be used to convince people who aren't already Catholics.
I have this crazy tendency when posting on a Catholic message board and discussing matters with someone who claims to be Catholic that I can take the Catholic philosophical framework for granted.
It is impossible to come up with a single argument which would be convincing to everyone. You have said that consciousness and self-awareness are valuable, but that is hardly a universally agreed upon statement. In fact I know that the author Peter Watts (of Blindsight) disagrees with it, and only sees survival advantages as valuable (and he does not think that consciousness or self-awareness has any significant survival advantage). In fact there is no universally agreed upon notion of value.
And if there is no universally agreed upon notion of value, I can hardly create a universally convincing argument for why any particular thing is valuable, can I? It is necessary to know the beliefs of the audience and to either build upon them, or to start by changing those beliefs if they are completely false.
This is why it is so important to start any philosophical discussion by looking for common ground.