I think that with a Native English speaker you are going to learn the most grammatically correct way to speak the language and you can pick up some really useful English phrases that Native English speakers use every day such as colloquial terms, idioms, slang and more casual as well as formal conversation.  I'm talking about phrases such as:

Quite a few

Well off

To hear of

To go off

Might as well 

In my opinion, no one knows the English language better than a Native English speaker and no one can explain it better.  I am sure a student or teacher who is proficient in the language can do a very good job, however, are they familiar with all the latest phrases and meanings? (English words and phrases are constantly being updated and modernised, language never stays the same.)

To answer <a ui-sref="user({id:comment.commenter_obj.id})" href="https://www.italki.com/user/4267720" style="background-color: rgb(255, 255, 255);">Paweł Targoński</a>'s question about native but inexperienced tutor vs C2 non-native tutor...

As a beginner, I would be very careful with inexperienced tutors. While they have the best intentions, some native speakers really cannot teach beginners. Many on iTalki can, but I've also met some that can't. I've had tutors who had no idea how to "dumb down" their way of speaking to fit my level and struggled to use simple vocabulary and grammar. It seems easy but teaching--especially teaching beginners--is honestly an underrated skill. For beginners, professional teachers with language training (whether native or non-native) may be better suited than a tutor with no experience.

I will admit that there are some things in my native languages that I would not know how to explain or different word usage that I'm not even aware of, and it always amazes me to hear the language being explained from a non-native perspective. Learners really can gain something from other non-native speakers. Concepts that a native would say "Idk that's just how it is!" can be broken down and explained by someone who had to actually study that concept.

Nowadays, maybe the most People are looking for native speakers and I can understand it, but I completely agree with Camilo.

Spanish is my mother tongue and I speak of course fluently, but I could teach better German because I have been learning German for the last 10 years and I know the grammar rules much better than the spanish rules.

However, I have great respect for the teachers, who are teaching their own language and I am sure they know well the grammar and the way to teach it.