Maximum flow with Edmonds–Karp algorithm

Question

I am learning Edmonds–Karp algorithm , I formed following flow network, (capacity is described above arrow, where s is source and t is sink.)

If we first follow path S - A - C - T , we will get max flow equals to 1 as we cannot take path S - B - C - T (residual flow from C -- T became 0). I am also assuming that while doing BFS when we reach to t from c, we are stopping our BFS search and returning path. There is D left in the queue but we will ignore it as we have got one augmenting path. On next iteration we will move to B as S -- A edge residual capacity is 0.

If we first follow path as S - A - D - T and then S - B - C - T , we get max flow as 2.

I think, I am missing some basics, I belive algorithm does not dependend on which path I take first.

Thanks in advance.