Confusion on the M<>S Deduction

There seems to be a contradiction in the deduction that M&S must always go together. In the video, the first rule and contrapositive written out are M(g) -> P(g) and S(g) with a contrapositive of P(t) or (S(t) -> M(t). The second rule and contrapositive are M(t) -> S(t) and S(g) -> M(g). The video uses this to conclude that M&S always go together. However, doesn't this mean that the first contrapositive must be incorrect? Because based on the first contrapositive, we could have P(t) and S(g) that is sufficient for M(t); however, the second contrapositive tells us that S9G0 is sufficient for M(g). So, you can see how these two contrapositives are at odds. So, I'm wondering if there was a mistake in writing these rules or how to use them given that they don't seem to match with each other logically.