Milk is a bad analogy because the earth's bulk, mantle and lithosphere, is solid. But the mantle - because of pressure and temperature - is not rigid, rather ductile. As such, it slowly (cm/year) convects as a solid body, and this convection is thought to play a (minor) role in driving plate tectonics.
Mantle material rising under (and thus partly melting because of pressure release) and erupting at mid ocean ridges form new, hot oceanic crust. That cools and gets denser as it spreads until it finally is so dense that it sinks back into the mantle, forming a new subduction zone. A soft, partly (a few %) molten layer called Asthenosphere allows for this. In contrast to the ocean ridge the partial melt in a subduction happens because of fluid injection.
Now what about continents? While the ocean floors around are constantly constructed in mid ocean ridges and destructed in subduction zones, limiting ocean floor age to about 200 million years (and supporting the notion of recycling processes and cycles at work), continents are of a less dense material that floats around without subducting. The oldest rocks on earth (current record holder 4.3 billion years are on continental crust and they have already been through something.
We said continents don't subduct, at least not like oceanic lithosphere, but when continents collide after the ocean parting them has completely subducted, they get stacked and folded, some parts pushed up others down, which thickens crust and lithosphere and forms imposing mountains and elevated plateaus, like the Himalayas today. See this link for a visual approach to what happens when continents collide.
Can they come out again? No, not just like that. Continental material that gets into some depth because of the stacking comes under metamorphism which exists in different forms, but essentially means the rocks are transformed under pressure and heat. The mountains on top weather away and flow out at the sides under the forces of erosion and gravity, and even the lower storeys, the metamorphic rocks, can come to the surface again (remember, they are less dense than the underlying mantle material, they have a tendency to rise) and be exposed to weathering and erosion.
Continents do not subduct. They can collide and form huge mountain ranges. These weather and erode over time.