Would adding paragraph about the motivation provided by someone who doubted me to my final year project acknowledgment be unprofessional?

I would refrain from adding this to the written/electronic version of the project report. It's very personal and uses colloquial language that should be avoided in a formal report, even in the acknowledgement section.

Having said that, you may still give to that particular teacher a copy with your personal hand-written dedication.

Btw, great example of negative motivation (or what it's called): a negative comment with positive result.

I certainly think it could be worded in a more positive and professional way. It comes off a bit salty and as if all your research work was to prove one man wrong. If I were to read your work, I would certainly get a bad initial impression.

I originally wrote this as a comment, but as I am seeing different opinions in several answers here I feel like I need to write a full answer:

Although it could feel cathartic to "stick it" to this teacher (who was clearly quite rude), it probably isn't worth it, and definitely is not worth showing it to this particular teacher.

Don't do this. No, it is not professional, it won't gain you anything.

People who know your situation might think it's funny - these are the people you should share this with, in another context, or anonymously somewhere if you are looking for some validation. Post it on Reddit under a throwaway, let people comment on it here.

People who don't know your situation well, or who have a positive predisposition toward the person you are referring to, or just don't know you are likely to have a different opinion. They might see this as petty, vindictive, or just disrespectful. It just isn't worth your trouble.

If this teacher was that rude to you, unless you think it was intended as motivation, they've shown they aren't worth your time at all anymore. You achieved what you wanted to achieve - move on and be your own person.