It is well known that exist knots which are not slice, however I came up with the following argument contradicting this fact and I fail to see where the mistake is, can somebody help me?
Let $K_0$ and $K_1$ be two knots in $ S^3 = \partial D^4$. Since $K_0$ and $K_1$ are homotopic in $D^4$ they are isotopic in $D^4$. By the isotopy extension theorem, we can therefore find an ambient isotopy $$F:D^4\to D^4$$ sending $K_0$ to $K_1$.
Now suppose that $K_0$ is slice with slice disk $\Delta\subset D^4$, then we conclude that $K_1 = \partial F(\Delta)$. This would imply that every knot is slice.