I would have to go with the intelligence/capability argument. If a child is handicapped to an extreme severity, then he's no more capable than an animal. Therefore, objectively, he would be no more valuable in any way.
I think you are forgetting the fact that humans are not objective machines. We are subjective and oftentimes irrational beings capable of love, compassion, sympathy, etc. It's simply not in our DNA to be objective. We our biologically wired towards certain behaviors, some of which happen to be irrational. One of those irrational behaviors is our tendency to place unconditional value on fellow humans. I'm no biology expert, but this tendency probably evolved and helped our species survive together. We don't always act objectively and logically and we weren't meant to, either.
So, objectively, a human may be as capable thus as valuable as an animal. However, humans are not objective by nature. We feel a love for others unlike no other animal. This love has helped us survive as a species, so I don't think we have any obligation to change. I get a chuckle out of a few posters here who claim they only act in the most objective way possible, claiming that they would value their son no more than an animal if he had extremely poor intelligence. We aren't meant to act that way and 99.9999% of all mentally stable wouldn't act that way; it's one of the perks of being irrational and subjective, I guess.
Also, while a lot of dolphins may have high intelligence, it's the capability that matters imo. Primarily, communications is what's important. There may be animals with extreme intelligence, but they lack the tools to effectively communicate their thoughts and ideas. That alone drops the value of many of these intelligent species below that of humans. So, even objectively, how valuable is intelligence if it can't be practically seen by others?