1.There is a cause for the existence of something.
2.There is causality.
3.There is a cause for the existence of causality.
4.Let's assume the cause A for the existence of causality.
5.A -> existence of causality.
6.It is contradictory to say that A, which is a cause within causality, exists before causality exists.
7.A does not exist.
8.Statement 7 contradicts statement 3.
9.Statement 3 is derived from statement 1.
10.Statement 1 is incorrect.
Note: The OP's question is basically Kant's third antinomy which contradiction led to his formulation of transcendental apperception to resolve.
One approach to refutation of the contradiction follows here, as summarised in J. Backman's The Absent Foundation, page 12
As Heidegger emphasizes in his 1949 foreword to “On the Essence of Ground,” while the ontological difference and the nothing are not mutually “equivalent” (einerlei), they nevertheless belong together as the self-same issue (das Selbe) for thinking—as Being.
Being aka nothing – in contradistinction to beings which exist – is the ground, or ab-grund, literally 'ground-less', translating as 'void', in which beings come to presence. The beings themselves exist on the basis of reason and understanding according to Kant's unity of transcendental apperception. Being, the ground, does not depend on reason; (hence 'nothing is without reason').
pages 15 - 16
Here he also notes that in 1929 he did not listen attentively enough to the wording of Leibniz’s principle.48 To say that nothing is without reason or ground is assuredly a metaphysical statement, but if instead we emphasize the word nothing (nihil), we get: nothing is without ground. Being as the no-thing-ness is the ground, more precisely, the absent ground, which itself has no ground.
Reinterpreting the OP's problem:
Re. 7. [cause A for the existence of causality] does not exist.
Being (as nothing), does not exist.
3. There is a cause for the existence of causality.
Being is the ground of beings and hence causality.
8.Statement 7 contradicts statement 3.
No contradiction.
Causality is a description about the way that processes evolve, not a process. Insofar as causality has an associated process, the associated process is the idea of causality. Ideas are a particular pattern of thoughts.
In light of this, 4 is a priori false (at a minimum, thinking about anything requires something that thinks) unless A is identical to "a person thinking about causality". Thus 5 is either false or tautological (A implies A). If 5 is false, 6-10 are meaningless. If 5 is tautology, 6 is false (tautologies can't be contradictions) and 7-10 are meaningless.
David Gudeman's comment that you have not justified 6 is correct but unnecessary, since the claim that 5 is a contradiction cannot be true regardless of justification.
What is causality? Causality is a why question to predicate.
So, if you have statements with predicate in core only, you ll got a chaine of statements glued by logic, that called sophistics. And you ll got disprove of the predicate in the end. “O friends, there are no friends” - or something like that.
Because the problem, that you didn't frame the area where the rule(your statement) works. If the rule is everywhere - it has no cause to be.
So, what should you do?
