Central idea of Buddhism Is the central idea of Buddhism about being totally objective, see things as what they are and don't have a preference or judgement? If that is correct, then why we should prefer the ideas in Buddhism to any other ideas. Isn't that already making a judgement? Am I misunderstanding anything?
The Central Idea of Buddhism is the cessation of suffering.  Everything else is a means to that end.

The goal is not to be objective, but rather, being objective can serve or be a milestone along that goal.  Here's how it works out.

We suffer because we are attached to desire.  Therefore, we let go of desire to stop suffering.  Since desire permeates our experience, when we let go of desire, we transform our experience.  This experience may still have desire, but we are not attached to it -- we see the desire as part of our experience and are not wrapped up in it.  This is "seeing things as they are" or "objectivity".  The subjectivity is there, but we're more aware of the subjective layer as something we add rather than part of the thing itself.

Judgments, preferences, and so on can still be there; after all, if the Buddha didn't have them, he would have just sat around until he starved to death.  However, we are not attached to these preferences and so on.  We don't get bent out of shape over them.

Why prefer this way?  Well, because you want to cease suffering.  If you don't care about suffering, there's no point in Buddhism.