That isn't a equivalent of this at all.

As you've understood it, no it isn't.

But the point was that a woman who signs an LPS is being asked to accept that if their mutual sexual activity leads to her getting pregnant, she's on her own if she doesn't choose to get an abortion. That contract is clearly biased in the man's favour. Likewise, the one I made up for illustrative purposes – so saying it "would never exist" was a bit redundant FYI – is clearly biased in the woman's favour.

How does the statement "I do not want to become a parent until I choose to become a parent" imply "I only care about myself and you don't mean very much to me"?

The statement doesn't – as you say yourself, "Couples have discussions like this" all the time and I agree, they do.

What they don't do all the time is have the man ask his partner to sign a contract to the effect that he doesn't want children more than he wants to stay with her, and that this is so important to him – and him alone – that he insists she sign away any legal claim she might have over him should she get knocked up.

Discussions like this do not imply that the two people don't care about each other.

Discussions, don’t, no, but a contract of the kind you are describing clearly does indicate that – how can it not? He is making her sign a binding legal agreement that says he will cut her off if she chooses to have a baby they did not plan on having.

A zero sum game?

Yes. The LPS contract you describe, if signed, would be a gain for you over your partner to her detriment. You seem to have this idea that the relationship is all about her having power over you ("unless she retains that power over you", " you become my slave", "signing away the right to control yourself",).

So much so, that you find the idea of a contract that offers you legal protection from having to make compromises or change your life plans if your significant other gets pregnant.

That strikes me as being a sign of anxiety and a desire to control that anxiety by controlling the social environment that surrounds someone.

(I have found this discussion quite enlightening by the way - I must have been doing it on and off for about 3 hours now(!) - so I hope you're not offended by anything I've said as I've obviously enjoyed it).