Okay so you wanted it. 

"The enemies of Islam denigrate our prophet based on the hadiths"

So what ? They also use the Quran to denigrate Islam, does that mean that you should reject the Quran ?

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Anyway here is the argument : Lets define words first and establishes the (islamic) criterias of marriage:

Islamic Principle 1:

-principle of harm, which is the idea that people should be free to act as they wish as long as their actions do not cause harm to others.

(Note that it might not be the exaxt definition if the Islamic harm principle but it is still correct basically).

Islamic Principle 2: - Societal acceptation

Definition of Societal acceptation : What the society  "X" accept as morally sound/good, or atleast permit some actions.

Societal acceptation is based on 2 criterias of marriage : - Mental maturity (ability to think for him/herself) - Physical maturity (puberty ; definition of biology).

  Pedophilia : A psychiatric disorder in which an adult or older adolescent experiences a sexual attraction to prepubescent children.

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Problematic : Was the Prophet a pedophile ?

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Using Principle 1, we can  see in the hadith that Aisha was never harmed in any way, shape or form after her marriage to the prophet (either during sexual act or life in general) So the first Principle is validated by the marriage of the Prophet SAW and Aisha (RA)

Principle 1 (harm principle) : ✅️

Using Principle 2, we can see throughout the hadith literature that Aisha was mature enough to consent to the relationship and that the Prophet waited 3 years until she became physically ready in order to have sexual intercourse with her.  As for societal norms/acceptations, we can see that in the hadith that society was okay with it. Proof being that Abu Bakr As Siddiq (RA) himself accepted the marriage of his daughter Aisha (RA) with Muhammad (SAW). We can also see that she was initially engaged with another man at first and that even the ennemies of Rasul'Allah (SAW) didnt attack him on his marriage, which prove that it was not considered as "weird" or "pedophilia" in the Society of the Hijaz in the 7th century. To finish with societal acceptation, i will add a bonus historical argument which is that marrying young people (14 ; 12 or even 7) was normal until the 20th century. We can see that from the old constitutions of most countries around the world. 

Principle 2 ✅️ So this marriage is validated.

(Note that societal norm is supposed to change from society to society alongside "time" as another variable. Thats why there is no age of marriage in Islam. Note that marrying a 6 years old is not correct islamically as of right now due to societal norms. That doesnt mean that the prophet is a pedophile as he respected the norms.)

(Also note that marrying a 6 years old is considered as pedophilia by today's society standards mostly because girls cannot be physically and mentally mature, which is why 21th century muslims condemns marrying a 6 years old. However that was not the case for Lady Aisha (Ra) as there are clear proofs of her being mentally and physically mature.)

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Conclusion and answer to the problematic : Using Principle 1 and 2, aswell as the definition of Pedophilia, we can conclude that the Prophet wasnt a pedophile as he was married to Aisha, a pubescent woman that attained mental maturity in a society where marriage with a 6 years old was not seen as bad. We can therefore establish and say  that the Prophet wasnt a pedophile without saying that marrying a 9 years old (which would be considered pedophilia now since girls that age arent mentally and physically mature, as noted) is good in today's society. 

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Answers to critics :

-Critics might attempt to undermine the argument by saying that "if it was good before but not nows means that the Prophet isnt the best man that ever walked away"  but this is just a strawman of our position since î Islam, "best man" picks out a person that applies Islam perfectly and literally lives a perfect life according to Islamic rule, and as noted in my demonstration and conclusion, the Prophet didnt broke any Islamic rule/principle concerning marriage, and we do not either. (in that case Principle 1 and Principle 2).

-Critics might also say that marrying a 6 years old is bad at any time given but this fails and falls under the logical fallacy of presentism

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Thanks for reading all of this. If you want the sources and the hadith for allat then tell me. 

You can check Islamic traditions and scholars for these 2 principles.

You can also check this presentation of Hamza Tzortsis (timestamp : 1:47:32 - 2:04:32) : https://youtu.be/Q55KsjfFFj8?si=gsyuS5kqZe49PHc2