Is it wrong to write a sentence by "First, ...." at the beginning of the sentence?
why would I ask the question because when writing my thesis, my professor prefer me writing "Firstly" instead of writing "First".

Question

Is it wrong to write a sentence by "First, ...." at the beginning of the sentence?  
why would I ask the question because when writing my thesis, my professor prefer me writing "Firstly" instead of writing "First".

Answer

You can use both 'first' and 'firstly' to begin a list of reasons or arguments or to say in the first place/ before anything else or to list how things happenend or how they will happen.   'Firstly/ first, this car looks awful and secondly/ second, it's unreliable. 
Most people think that If you begin with 'firstly',  you should continue with 'secondly' and if you begin with 'first' you should continue with 'second' and not mix them up.
 
'Firstly' has become less common and some think it is more formal.

Answer

It's perfectly OK to start with with 'first'.

Answer

No. It is perfectly fine to start a sentence with first.