Unfortunately by still eating dairy and eggs, you are participating in that system.

Who says they eat dairy and eggs? “Vegetarian” isn’t such a simplistic label like that. It doesn’t mean “I eat exactly these things”. For all we know, they eat only eggs and from a local farm (or have their own chickens).

Furthermore, it’s a bad argument to imply vastly reduced complicity with a system is the same as full complicity.