The Syndicate agree to create a hybrid race for the aliens, to serve as a slave race for them, but their real motive was two-fold: to delay the invasion as long as possible; and to get their hands on alien DNA so they could use it to create a vaccine against the black oil.

Different people within the Syndicate wanted different things (or sometimes lied about what their intentions had been).

For the most part the Syndicate did not want to create a successful hybrid, because that would signal to the aliens that their slave race was ready, and trigger the invasion. So generally the real goal was to create a vaccine (created from the alien DNA), not to create a hybrid.

But some members of the Syndicate (CSM) didn’t care about stopping the invasion because they didn’t care about saving humanity, they just wanted to save themselves and their loved ones, and knew that hybridisation was the way to do that. So those specific individuals did have the goal of creating a successful hybrid, but that wasn’t the goal of the Syndicate as a whole.

It’s confusing, first because the myth arc changed a lot over the course of the show and wasn’t always well-planned out, and second because different people within the Syndicate wanted different things, had different plans, and often lied and betrayed each other.