An inseparable sequence is an almost disjoint family $\langle A_\xi:\xi<\omega_1\rangle$ of subsets of $\omega$ such that for no $D\subseteq\omega$ there are uncountably many $A_\xi$ such that $A_\xi\cap D$ is finite and uncountably many $A_\xi$ such that $A_\xi\setminus D$ is finite. We investigate under which conditions is an inseparable sequence destroyed by forcing. We translate these conditions into forcing language and use them to obtain several necessary conditions for destroying inseparability. In particular, we prove that in order to get such a notion of forcing with c.c.c. we must assume at least $\neg$MA, and in order to get such a notion of forcing that is proper we must assume at least $\neg$PFA.