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In my understanding, the argument at a certain place goes as follows:

  1. All synthetic judgements that can be true are about possible experience.
  2. All necessary conditions for existence of possible experience are satisfied in every synthetic judgement that can be true.
  3. We can therefore talk about these necessary conditions of experience with a priori judgements, and they happen to be synthetic.

Why are they synthetic?

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  • Because he started by selecting out only the synthetic judgments in premise 1. That is what he is discussing. He is not saying all judgments are such, but he finds it significant that any of them are. Clearly, the parts that combine actual experiences are not a priori, by definition. And the parts that are analytic, Kant took as too obvious to address (a mistake, given what we now know about the fragility of logic) So what he thought was worth worrying about first was the synthetic a priori, the chicken-and-the-egg part.
    – user9166
    Feb 21, 2017 at 17:57

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For analytic statements we cannot conceive the possibility that they can turn out to be false. The statements that Kant characterizes as synthetic aprioi are (mostly, if we put mathematics aside) not of this nature. Take for example the law of causality: every change has a cause. We can apparently conceive that an event (say, a sudden rain in a summer day) will happen without any prior cause. This was indeed part of David Hume's theory of causality, which deeply influenced Kant. Nevertheless, Kant claimed that every event does have a cause, and necessarily so. And since the opposite can be conceived, that necessary statement is synthetic. 

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