Question: I recently have had a discussion about my friend's tone in his email.

His supervisor asked him whether he wants to attend a summer school in May. He wanted to thank him for his invitation and also wanted to keep the mail short. As a result, that is what he came up with:

> 
> Hello Professor,
> 
> 
> I have plans during that period. Thanks, but no thanks.
> 
> 
> Regards,  
> 
>  John 
> 
> 
> 

He is getting along well with his supervisor, but I believe that the phrasing is a bit disrespectful nevertheless. It might be the case that I am not a native speaker. 

Am I exaggerating the situation and this is something can be overlooked?

Answer: 
It's not the use of a "slang" expression that's the issue.

Saying "thanks, but no thanks" implies that s/he was trying to trick you with the offer to which you're replying. The phrase is imbued with a bit of hostility and disdain.

So, don't use it. Also, the way your friend phrased your email sounds flippant. Turning down an offer from someone's advisor should be done with more of a justification. It wouldn't hurt to be **polite and respectful**, and write something like

> 
> Hello Professor Smith,
> 
> 
> I want to thank you for the offer of XYZ; unfortunately, I've already made plans to [important activity that clearly should not be canceled to take the offer].
> 
> 
> [Possible counter-suggestion regarding the offer, e.g. doing something after that period of unavailability.]
> 
> 
> Regards,  
> 
>  John
> 
> 
> 

Still pretty short.

Notes: 

* The reason doesn't have to be super-specific, but the more vague it is, the more it's likely to sound like an excuse.
* If your friend dislikes his/her supervisor, or doesn't appreciate him/her, or the offer - that's *double* the reason to be polite and respectful of him/her when rejecting.
Your friend seems to have gotten the idea that "no thanks" is needed to indicate that the answer is "no", while "thanks" is needed to indicate gratitude for the offer. That is not the case. If the email were to contain nothing but the word "thanks", that would be inferred to be acceptance, but "thanks" in an email that otherwise indicates other plans would be understood to be only gratitude, and not acceptance. And "no thanks", as the words indicate, communicates both a negative answer and gratitude. 

Thus, "thanks, but no thanks" is redundant. Unfortunately for your friend, it is a form of redundancy that has been used to indicate disdain. To be precise, I would say that it not so much *is rude*, but has been associated so much with rude intent that it should be avoided (although of course there is a point at which "is taken to be rude" becomes the same as "is rude").

You say that you are not a native speaker, but don't mention whether your friend is. If I were speaking with a non-native speaker, I would give them the benefit of the doubt and not expect them to be familiar with the entirety of English-speaking culture. Even with a native speaker, I would be willing to entertain the possibility that they chose their words poorly without considering the pop-culture context, especially if I had had previous dealings with them in which they were polite. Other people here have indicated that they would be less charitable, which I find unfortunate, so your friend will have to consider the possibility that the professor will share their attitude.