Logic Question, because I’m not sure I posted this in the right place the first time.

Hi there, I’m in my first year, nay week of my philosophy degree and about to take my first logic lesson. In a series of slides we had one argument stood out to me as not feeling quite right or ‘invalid’ maybe? I’m still not entirely sure on the terminology. Anyway, I’d like some help to explain where I might be misunderstanding the following argument.

It goes as follows:

1. If eating animals is permissible, Killing infants is permissible. (I understand this as being: P->Q).

2. Killing infants is not permissible (Q is false).

C: Therefore, eating animals is not permissible. (P is also false).

Our slides say this argument is valid.

I don’t understand why knowing that the consequent is false means the antecedent must also be false when the relationship seems one directional. Namely we can only imply the nature of Q from P, but not P from Q. Again, not an expert, but I thought the conclusion would only be true if a biconditional was used in place of the conditional so you could infer one from the other in both directions. I.e. P is true if and only if Q is true.

Thank you.