Why Turkey's president thinks that by cutting interest rate it will lower inflation? Recently, President Erdogan sacked the head of Turkey’s central bank because he didn't want to cut interest rates. He even said: “We said that if rates fall, inflation will fall. He didn’t do what was necessary.”

From my understanding of economics, this is the opposite of how things work. If we want to lower inflation, we should raise interest rates even further. So why President Erdogan is conviced of the opposite? Is there a sound economic theory that would agree with Erdogan's initiative?
I'm gonna start this off by saying this is speculative, so take this answer with a grain of salt.

In order for a counter intuitive measure like this to work, there must be something else going on that over-shadows it. (Inflation topics tend to be riddled with things like this). I admit I don't know what the economic climate in Turkey is like currently; but I can think of a way that it would make sense to lower rates and expect lower inflation. 

In light of recent events, Turkey has been the focus of some very negative media coverage as of late, and some of it for good reason. The last couple years for Turkey have been rough to say the least; but that's not the macro-trend of Turkey.
Turkey is an emerging market economy, they have urbanized dramatically from 2000-2015, maintained strong macroeconomic and fiscal policy frameworks, opened up to foreign trade and finance, harmonized many laws and regulations with European Union (EU) standards, and greatly expanded access to public services. It also recovered well from the global crisis of 2008/09.

Tying this back to your question now, it could be the case that Turkey's government spends too much money and is the biggest factor in the inflation numbers. If President Erdogan can better enable the people of Turkey to replace the effect of government spending organically (enable the people via lowering interest rates), then he can purposely scale back government spending (which would lower inflation b/c it's the bigger factor). 

In summary: Erdogan may be trying to stabilize Turkey's economic climate via lower government spending which will reduce aggregate demand, leading to lower growth and less demand pull inflation. The macro trend of Turkey and forecasted growth expectancy is very high, and probably over heated, despite the recent negative issues in the micro economic climate.