How come water in a cup won’t shoot out of a straw placed inside it?

I’ve been learning about pressure and fluid dynamics, and I’ve stumbled onto a problem. Say you have a straw in a cup. The surface area of the water in the cup is much greater than that of the straw. So I would expect Atm. Pressure × Large Area gives a much greater force than Atm. Pressure × Small Area. In fact, the force is so much larger I would expect a spectacular jet of water, which obviously does not happen.

What am I missing?

Thanks

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