Let ϕ(x) means "x is married." Then you can find a group of people that includes both marrieds and singles and call one married person x.

I assume that the definition of logical consequence requires evaluating the two formulas (on the left and right of ⊨) in the same structureand the same valuation. Then you can make ∀x. ϕ(x) true and ∀x. ψ(x) false in some structure and choose the valuation that makes ψ(x) false.