Plato's Phaedo

Let us first take for instance the notion that the body is a prison for the soul. That is explicitly a Pythagorean ideal. Also in this dialogue the play on contraries is also a Pythagorean geared argument. The focus on Pythagorean ideals is also important considering the narrator, Phaedo, is also a Pythagorean. Without understanding this, the bias of the narration would be missed entirely.

The dialogue is not so much Socrates telling Simmias and Cebes what actually happens to the human soul, but is more of an attempt to calm them and to make his last moments alive pleasant. The Pythagorean approach which is heavily based on mathematics (body + soul = life) will not prepare someone to handle their own death. Socrates is explicit about this in his allusion to the second sailing. Even if one views death as the separation of the soul from the body, it will do little good to explain what actually happens. Actual life is not like an equation where once a body and soul are split, they can simply be brought back to life by the addition of them again.

The arguement isn't that Socrates is defending the immortality of the soul. The argument is that Socrates is trying to console Simmias and Cebes who would be devastated to think that the soul dissolves at death. The dialectical argument is geared towards Simmias and Cebes who have a way of understanding the world that will not explain death. Socrates is not teaching Simmias and Cebes about the immortality of the soul. Instead, Socrates is teaching Simmias and Cebes how to die, which they ultimately will have to do.

Platonic 'Forms'

In the Platonic dialogs, Socrates uses forms to demonstrate that people use 'forms' to justify arguments (such as Justice, Good, Noble). Socrates demonstrates that these 'forms' weren't gathered from the senses. You cannot see Justice, but only reason about it. The separation of the senses from the 'forms' is what gives the 'forms' special consideration from knowledge obtained by the senses. This means that 'forms' can be more susceptible to human longing.

In many ways 'forms' are anti-philosophical. They are the projections of the soul (better understood as pure thought) being a slave to the body. People will want something and invent something like love to explain and justify why they are doing this. The dialogs do not say forms exists but only that they exist out of human thoughtfulness that is distorted by the body. We do not see reality directly but only through special lenses. Forms are an invention of the human imagination to make life relevant to how are able to interact with the world.

Furthermore, It is well understood that Socrates makes bad arguments on purpose. The Socratic method is all about putting forth an argument and refining it and not about making an airtight thesis. All the arguments that Socrates' companions bring up require an assumption that forms exist. If you read closely, you will find that Socrates is quite critical of forms. While Socrates is arguing with his friends. He defines the argument as other people present it or how things are commonly thought about. Near the end of the dialogs Socrates then, after his friends still do not understand they are being foolish, offers a parable of some sort showing how reason is limited to certain things that pertain to how humans think. His friends still do not understand but we as readers can more easily recognize their foolishness.

Simply put, the tradition of philosophy that was started by Plato is a pursuit of knowledge with the understanding that reason is part of being a human and is not actual reality. This differs drastically from what maybe seen as the scientific pursuit of knowledge which tries to separate the human component of knowledge meaning that what science discovers is not part of human reasoning but an actual law of nature outside and independent of human thought.