US Treasury yields and equity prices

I am a bit confused about what is going on in the markets right now. To my understanding, rapid increases in Treasury yields have prompted equities selloffs. However, bond yields only go up when prices go down, correct? And prices go down when people are selling bonds faster than they are buying them. It seems to me that the only reason for a selloff would be optimism in the future economy and rising inflation expectations.

But if people are optimistic and selling bonds, why are equity prices decreasing? Surely the same people who sold the bonds and are optimistic would put money into equity markets, leading to higher prices? I understand that higher bond yields lead other investors to think about moving capital there, but how can bond yields go up and stock prices go down at the same time? Wouldn’t the demand for bonds quickly cap the rise in yields (and lead to yields falling again)?