I'd like to propose a different way of looking at the possibility of confusion between chicken and meat.
Most people explain the problem is that the Rabbis decreed that chicken can have a Halachic status of meat, since it is similar in appearance and may be confused with meat. If so, why wouldn't such a decree apply to all things that may be mistaken for something else. As was asked in the question, should soy milk also be considered like real milk?
However, if you explain that the Rabbis were worried about confusion resulting from a logical mistake (and not a mistake in appearance), you could understand why chicken is Rabbinacally considered like real meat while soy milk is not considered like real milk.
To explain. Just like meat, kosher birds have a biblical obligation to be ritually slaughtered and salted. Just like meat, if one of these steps is not done properly, the bird is unfit/forbidden to eat. However, there is no Biblical problem with eating kosher birds with milk.
The Rabbis saw that people were making a logical error and saying, "If a bird that must be slaughtered and salted may be eaten with milk, the same thing should also apply to a kosher animal that must be slaughtered and salted. The animal should also be permitted to be eaten with milk."
Once the Rabbis saw the logical mistake people were making, they banned the practice of eating fowl with milk, so that people would not mistakenly eat animal meat with milk.
I don't have a source for this, but the Taz in Yorah Deah 81:6 S"K 9 uses similar logic to explain why it is forbidden for an adult to drink breast-milk directly from the source. The Taz explains that the reason it is forbidden is because "you may come to switch it with an impure animal", which I understand to mean that you may make a logical mistake that if milk from a person (who is impure - i.e. may not be eaten) may be consumed, I might come to conclude that milk from a nonkosher animal may also be consumed.
I just saw the Rambam, Hilchot Mamrim 2:9, where the Rambam explains the decree forbidding chicken and meat was to prevent a logical mistake. He has a different logical mistake people could make. He says:
...the court says: "The meat of fowl cooked in milk is permitted according to Scriptural Law. We, however, are prohibiting it and publicizing the prohibition as a decree, lest the matter lead to a detriment and people say: 'Eating the meat of fowl cooked in milk is permitted, because it is not explicitly forbidden by the Torah. Similarly, the meat of a wild animal cooked in milk is permitted, because it is also not explicitly forbidden.' "And another may come and say: 'Even the meat of a domesticated animal cooked in milk is permitted with the exception of a goat.' And another will come and say: 'Even the meat of a goat is permitted when cooked in the milk of a cow or a sheep. For the verse mentions only "its mother," i.e., an animal from the same species.' And still another will come and say: 'Even the meat of a goat is permitted when cooked in goat's milk as long the milk is not from the kid's mother, for the verse says: "its mother."' For these reasons, we will forbid all meat cooked in milk, even meat from fowl."