The problem is that heat flow (in or out of an object) is related to the temperature difference between the object and it's environment. For the sort of cooling usually found in the kitchen (convective cooling) the heat flow, and therefore the rate of temperature change is proportional to the temperature difference.
So let's take some example like a bottle of milk. If you want to heat it quickly that's pretty easy because it's easy to generate a large temperature difference on the hot side. Just burn some gas.
However to cool the milk quickly we need to generate a large temperature difference on the cool side, and that's hard. You mention liquid nitrogen, and indeed that's a good way to cool things quickly. However you're forgetting all the hours the liquid nitrogen supplier had to put in to cool nitrogen enough to make it liquify. In general it's hard to cool things quickly unless you cheat and start with something (like liquid nitrogen) that's already been cooled.
Response to comment:
This started as a comment, but it got a bit involved so I thought I'd put it in here.
The temperature of anything (e.g. milk) depends on how much heat it contains. Let's not get into exactly what heat is, but basically if you add heat it increases the temperature and if you remove heat it reduces the temperature.
The problem is that the milk is surrounded by the rest of the world, and this is around room temperature. Heat won't flow from a cold place to a hot place, so heat won't flow out of the milk into it's surroundings unless we do some work. Typically what we do is use energy to pump heat around. The area we've pumped the heat from becomes cooler and the area we've pumped it to becomes hotter. This is what you do to liquify nitrogen. You have to pump the heat out of it so te nitrogen gets cold and liquifies while the rest of the world gets hotter. Once we have the liquid nitrogen we can use it to cool the milk, but it took a lot of work to make the liquid nitrogen.
If you're interested in pursuing this, the mechanism for pumping heat around is called (unsurprisingly :-) a heat pump. It's basically a heat engine that runs backwards.
Heating things is easy because there are lots of systems that have stored energy that can be easily converted to heat. For example a gas/air mixturer has chemical energy that is converted to heat by burning it. You mentioned a microwave: this uses electricity that came from chemical energy i.e. from a power station burning gas or coal, so the heat froma microwave originally came from chemical energy.
You might wonder why we can't easily convert heat to chemical energy e.g. mix carbon dioxide and water and have it convert to gas and oxygen and cool down in the process. If we could do this it would be an easy way to cool things. The reason why we can't do this is the second law of thermodynamics. Explaining this would be a long essay in it's own right, but in brief it's highly probable that a gas/air mixture will convert to carbon dioxide and water (i.e. burn) but it's very improbable that a carbon dioxide/water mixture would convert back to gas and air.