Here's how the ten two-color archetypes ended up:

White-blue (artifacts) – The Phyrexians have always been tied to artifacts, so it only seemed right to have one draft archetype focus on them. Blue is primary in "artifact matters" and white is secondary, so those two colors seemed like the best choices.

Blue-black (proliferate control) – Blue is one of oil counter colors. Black is one of the poison counter colors. Put the two of them together, and you have your normal manipulative blue-black deck, but now with a dose of counters and proliferate.

Black-red (oil counters and sacrifice) – Sacrifice is a common black-red archetype. The set adds in oil counters to the mix and creates a two-color combination that feels quite Phyrexian, as they see death as a valuable tool.

Red-green (midrange oil counters) – Red and green are both oil counter colors and are the two colors that care most about how many permanents you have with oil counters. This theme works well with a deck that grows in strength over time as you gain in mana and oil counters.

Green-white (toxic aggro) – Green and white are two of the three poison colors. This deck makes a horde of creatures with toxic, including the Mite creature tokens, and swarms for a poison win.

White-black (corrupted) – White and black are the two colors with the most corrupted cards, so they come together to poison your opponent just enough to make your cards even more powerful.

Blue-red (oil counters and noncreature spells) – This deck uses your noncreature spells to gain more and more oil counters, which then create effects to help you win this tempo strategy.

Black-green (poison victory) – Black and green are the two colors with the largest toxic creatures. Get them out and win in just a few hits.

Red-white (For Mirrodin! Equipment) – Red and white are the two colors with the most Rebels in it. Use the Equipment with the For Mirrodin! keyword to aggressively attack.

Green-blue (proliferate and poison) – Green has a lot of cards that poison. Blue and green are both good at proliferating. Poison your opponent and then slowly proliferate them to death. This is the most controlling of the poison decks.

When you combine these five themes, you get the ten two-color archetypes:

White-blue – This is the combination of go-wide with instants and sorceries, so it's focused on generating a lot of tokens, protecting them, and then boosting them. Go wide strategies aren't traditionally done in white-blue, so this is pushing into novel space.

Blue-black – This is the combination of instants and sorceries and death. The end result is a control deck that uses card advantage to slowly eke out a victory.

Black-red – This is the combination of death and aggression. This results in aggressive creature strategy where you're rewarded for having your creatures die.

Red-green – This is the combination of aggression and ramp, so it's a mid-range creature deck that makes use of some domain cards.

Green-white – This is the combination of domain and go wide. This deck splashes extra colors to use domain as a tool to reinforce your attacking army.

White-black – This is go-wide plus death, which means it's a deck about creating a lot of small creatures that you then sacrifice for value. This ends up being a slower controlling deck than most go-wide strategies.

Blue-red – This combines instants and sorceries with aggression. That leads to a tempo-based spell deck.

Black-green – This combines death and ramp. This results in a mid-range deck that makes use of the graveyard.

Red-white – This combines aggression with go-wide that results in a typical aggro creature-based strategy, red-white's bread and butter.

Green-blue – This combines ramp/domain with instants and sorceries. It results in a base green-blue deck that splashes two to three colors and makes use of big domain effects.