It seems all or almost every philosopher who addressed the question seem to think that apriori knowledge exist, but I couldn't hear a single good argument that seeks to prove that apriori knowledge doesn't exist. What are some strong arguments that argue that apriori knowledge doesn't exist?
I am reminded of this passage from the preface to Kant's Critique of Practical Reason:
Nothing worse could happen to these labours than that anyone should make the unexpected discovery that there neither is, nor can be, any a priori knowledge at all. But there is no danger of this. This would be the same thing as if one sought to prove by reason that there is no reason. For we only say that we know something by reason, when we are conscious that we could have known it, even if it had not been given to us in experience; hence rational knowledge and knowledge a priori are one and the same.
As per the SEP article on the subject, there are many concepts/definitions of apriority. One wonders whether any of them are persuasive, either just as definitions or as applicable concepts. One might argue, then, though, that apriority isn't a real epistemic form, because the very distinction between apriority and aposteriority isn't a real epistemic distinction. That is, there isn't any empirical knowledge, either: knowledge is neither "rational" nor "empirical." Personally, I think we can usefully differentiate between a priori and empirical evidence/justification/etc., but this comes down, effectively, to a stipulation in a given system; give a different system and you give a different distinction, if you give one at all.
A priori knowledge can't exist because knowledge comes äfter encountering the reality you want to know about. Knowing how to sing means you have to sing first. Knowing how to use your vocal trackt means using it first. Knowing how to use it means using things first.
More generally, knowing a truth about any subject means that you have to interact with the subject first. Every interaction has it's own method. The knowledge of this method is not a priori known and neither is the knowledge of the subject matter one wants to know about. How could we know a priori? By means of biologically transmitted knowledge? It could be that the reflex to eat and the reflex to go to the mother's nipple are given a priori to the neonato. It could also be that already while developing this knowledge is aquired. The eye,for example, is already unconsciouly trained in the developing embryo. Cöncentric circles are being transmitted over the developing retina of the embryo to prepare the brain for the world waiting.
So it remains to be seen if a priori knowledge exists and to say honestly, I haven't encountered it personally. But everyone is welcome to make suggestions.
A priori knowledge is knowledge whose justification is not empirical in some important sense. The idea is that, with some propositions, once we have grasped what they mean, we know them to be true without having to test them empirically. It should not be confused with innate knowledge, which is knowledge we are born with or which is part of our biological endowment.
Of course, we need some experience of the world in order to have any knowledge at all, but that is not the point at issue. The crucial factor is what justifies it as knowledge. Lots of things have been claimed to be a priori knowable. Most philosophers historically have considered that mathematical knowledge is a priori, because we don't have to test mathematical propositions experimentally. We still need to learn mathematics, and we still need some experience of the world to understand it, but once we do, it is often considered to be a priori.
Some things that have been considered a priori knowable include logical or analytic truths (all squares are rectangles, all emeralds are green), fundamental moral principles (the golden rule), propositions that are guaranteed by the speaker's existence (I am alive, I am here now), and many others.
If you wish to argue against the possibility of a priori knowledge, your main challenge is going to be explain how we have knowledge of such things. It will probably require a piecemeal approach.
Quine has challenged the existence of analytic truths, and his arguments are in effect just as much arguments against a priority as they are against analyticity. That said, Quine still regarded logical truths as inviolable, at least in his later writings.
There are some who regard logical and mathematical truths as ultimately empirical in character. This position is called anti-exceptionalism. The idea is that the truths of logic and mathematics are akin to the laws of nature that we gather from science, but they are more abstract and topic neutral. They do not need to be tested empirically in a simple fashion, but ultimately they are justified by the contribution they make to our understanding of the world.
The a priority of moral principles could be rejected, from an anti-realist, relativist or even a moral naturalist stance on morality.
Propositions that are always true because of the speaker's existence are arguably merely anthropic and not a priori in any interesting sense. A person who says "I am here now" speaks truly, but doesn't say anything of any substance. Also, such a claim loses its a priority if it is de-indexicalised, or if it is used within an intensional context (my wife doesn't know I am here now).