(Q):
A single-cell lifeform that converts nutrients and oxygen into biological energy causing its cells to divide, multiply and grow, which also contains a full set of its own DNA.
Actually, a zygote is not a "single-cell lifeform", as it does not persist as a single cell forever, whilst a amoeba, on the other hand, never becomes a multi-cellular creature. Moreover, you seem not to take into consideration the taxodermic classification of either an amoeba or a human being, which clearly demonstrates that they are massively different.
From Wikipedia:
A zygote (Greek: ζυγωτόν) is a cell that is the result of fertilization. That is, two haploid cells—usually (but not always) a sperm cell from a male and an ovum from a female—merge into a single diploid cell called the zygote (or zygocyte).
Animal zygotes undergo mitotic cell divisions to become an embryo. Other organisms may undergo meiotic cell division at this time (for more information refer to biological life cycles).
Amoeba:
Amoeba is a genus of protozoa that moves by means of temporary projections called pseudopods, and is well-known as a representative unicellular organism. The word amoeba is variously used to refer to it and its close relatives, now grouped as the Amoebozoa, or to all protozoa that move using pseudopods, otherwise termed amoeboids. They are found in sluggish waters all over the world, both fresh and salt, as well as in soils and as parasites.
Amoeba itself is found in freshwater, typically on decaying vegetation from streams, but is not especially common in nature. However, because of the ease with which they may be obtained and kept in the lab, they are common objects of study, both as representative protozoa and to demonstrate cell structure and function. The cells have several lobose pseudopods, with one large tubular pseudopod at the anterior and several secondary ones branching to the sides. The most famous species, A. proteus, is 700-800 μm in length, but many others are much smaller. Each has a single nucleus, and a simple contractile vacuole which maintains its osmotic pressure, as its most recognizable features.
Early naturalists referred to Amoeba as the Proteus animalcule, after a Greek god who could change his shape. The name "amibe" was given to it by Bery St. Vincent, from the Greek amoibe, meaning change.
A zygote is a potential human, as it is in the same state as an ameba.
(Q), I find it hard to imagine that someone such as you, who professes science as the ultimate end of human knowledge, can hold such a semi-religious view of humanity. A zygote is no more a potential human than an infant is a potential human, scientifically it is a human being, genetically verified as such and in all ways fullfilling what makes a human, a human, scientifically. Please, don't interject belief here. We're dealing with science.
Exactly, but do we allow massive suffering to both children and adults simply because one of them might achieve something?
"Massive suffering" can only be determined by the individual who suffers.
Let's deal with this from game theory:
Assuming meaningful experience only outside the womb:
Abortion - Positive results: 0. Negative results: 0
Life - Positive results: Potentially infinite. Negative results: Potentially infinite.
So you have potential infinities of either positive or negatives, with a likelyhood of mixture of both extremely high, whilst one can basically not play the game at all with abortion. Since life also has the option to be ended at virtually any time by the self, you're not only depriving him of the chance for infinite gain, but of being able to decide if the negative truly outweighs the positive.
If I could see into the future as a zygote and realize that I'd be born with down syndrome, or into abject poverty soon to die of starvation, it would be a no-brainer, pull the plug now.
Your decision is utterly viable for yourself, but you cannot presume that this would be the same for all others.