There are two issue. One, the Quran does not set a minimum age of marriage. In fact, it suggests that men can marry female before they menstruate – that is before puberty!
In this verse, the Quran sets the conditions to when to have intercourse with women you marry – to ensure a child you get from them is yours.
“And those who no longer expect menstruation among your women – if you doubt, then their period is three months, and [also for] *those who have not menstruated* ….”
And then comes many authentic Hadith about the age of Aisha at marriage.
Narrated Hisham’s father: Khadija died three years before the Prophet departed to Medina. He stayed there for two years or so and then he married ‘Aisha when she was a girl of six years of age, and he consumed that marriage when she was nine years old.
Sahih Bukhari 5:58:236
Narrated ‘Aisha: that the Prophet married her when she was six years old and he consummated his marriage when she was nine years old, and then she remained with him for nine years (i.e., till his death).
Sahih Bukhari 7:62:64
Narrated ‘Aisha: I used to play with the dolls in the presence of the Prophet, and my girl friends also used to play with me. When Allah’s Apostle used to enter (my dwelling place) they used to hide themselves, but the Prophet would call them to join and play with me. (The playing with the dolls is forbidden for adult girls.) (Fateh-al-Bari page 143, Vol.13)
Sahih Bukhari 8:73:151
‘A’isha (Allah be pleased with her) reported: Allah’s Apostle (may peace be upon him) married me when I was six years old, and I was admitted to his house when I was nine years old.’
Sahih Muslim 8:3311
In total, 41 authentic Hadith that confirm Aisha’s age which you can find from Islamic sources:
And why is this a problem? Because the Quran is clear when it says:
“Indeed, in the Messenger of Allah you have an excellent EXAMPLE for whoever has hope in Allah and the Last Day….” Quran 33:21
In effect, what Muhammad did by marrying a child is giving a green light to every sick old man who wants to abuse a little girl to simply say “I am only following our beloved Prophet example”.