What is responsible for black tarnish on silver?
There is no such thing as "being reactive". Say, you have A and B; some compounds tend to react with A and not with B, and some would react with B and not with A. Which is more reactive? You can't tell; you can't even ask this question, for it's meaningless.

Black tarnish on silver is mostly silver sulphide, as confirmed experimentally. I'd even say that silver does not form a black film on being exposed to air, unless there is some source of hydrogen sulphide nearby (raw eggs, sewage pools, or something else).

It is just that $\ce{Ag}$ tends to prefer $\ce{S}$ over $\ce{O}$. Many other heavier metals are like that, and many lighter metals have different preferences. This is explained (kind of) by the hard/soft acids/bases concept.

So it goes.