There is a distinction between a sound argument and a valid one. A sound argument actually proves something. A valid argument may not. Instead, a valid argument preserves the truth of its premises.
The idea behind focussing on valid arguments in most logic is that any valid argument could be applied to a wholly different set of premises similar to the actual ones (in both form and truth value). And if those other premises were true, each set would produce a sound argument. So a valid argument can produce a number of different sound proofs. It is, therefore, more useful.
But if there is no truth in the premises, then absolutely any argument preserves 'all' of that nonexistent truth. So if your premises are false, your argument is always valid.
If your premises contradict, so that they cannot all be true, because if some of them are true, others would not be, then, taken together they are false. So your argument is valid.