In a Nutshell:
It began with the criticism presented by David Samuel Margoliouth (d. 1940) in his book, Mohammed and the Rise of Islam published in 1905.
Historical Background
The critics of Islam, before the 20th century, did not condemn the issue of the Prophet's marriage with A'isha nor his number of wives - whether this was the Quraysh, Christian and Jews in Arabia, Christian missionaries in Muslim Spain or any critic of Islam.
The eighth century saw the first writer to criticise Islam and the Prophet (saw) as John of Damascus in his book 'Heresy of the Ishmaelites' but he did not condemn the notion of marriage.
The eighteenth-century English historian, Edward Gibbon, wrote a chapter in his book 'The History of the Decline and Fall of the Roman Empire' about the life of the Prophet (saw) and he mentioned his marriage with A'isha (ra) at that early age but did not condemn it.
William Muir wrote an entire book on the life of the Prophet (saw) entitled 'The Life of Mohammad from Original Sources' and as a Christian missionary criticised the Prophet (saw) but he said nothing about the marriage age.
The famous Nobel Prize winner and Scottish philosopher Thomas Carlyle studied the life of the Prophet (saw) and not only failed to criticise the Prophet's marriage but said:
"It is a great shame for anyone to listen to the accusation that Islam is a lie and that Muhammad was a fabricator and a deceiver. We saw that he remained steadfast upon his principles, with firm determination; kind and generous, compassionate, pious, virtuous, with real manhood, hardworking and sincere. Besides all these qualities, he was lenient with others, tolerant, kind, cheerful and praiseworthy and perhaps he would joke and tease his companions. He was just, truthful, smart, pure, magnanimous and present-minded; his face radiant as if he had lights within him to illuminate the darkest of nights; he was a great man by nature who was not educated in a school nor nurtured by a teacher as he was not in need of any of this."
The eighteenth century critic of Islam Humphrey Prideaux wrote an entire book criticising Islam and the Prophet (saw) titled 'The True Nature of Imposture Fully Displayed in the Life of Mahomet' trying to disprove his Prophethood, but he found himself defending the issue of the Prophet's marriage with A'isha.
He said on the issue of A'isha's age at marriage:
Ayesha was then not six years old, and therefore he did not takeher into his bed till two years after when she was full eight years old. For it is usual in those hot countries as it is all India over, which is in the same clime with Arabia, for women to be ripe (reach the puberty) for marriage at that age, and also to bear children the year following. (Prideaux, the life of Mahomet, p. 52)
All writers and thinkers across Europe incincluding George Bernard Shaw, Simon Ockley, William Blackstone, Goldziher, Theodor Nöldeke et al, did not condemn this notion.
These two issues were historically and socially accepted because they could easily imagine a 9 or even 6 years old pride and this was historically and socially normal.
The rise of a new notion
After the 20th century, the world changed dramatically due to colonialism and growth of liberalism with new attacks and critiques emerging.
The British historian and orientalist David Samuel Margoliouth (d. 1940) was the first to raise this issue in history in his book "Mohammed and the Rise of Islam" published in 1905. He inked the first recorded critical statement of the Prophet's marriage.
His view resulted in increasing criticism of the age of A'isha (ra).
Some Muslim reformists were responding to his claim by rejecting the Prophet (saw) married A'isha when she was nine, claiming rather she was twelve or fifteen years old.
The first leading proponent of this view was the Egyptian writer Abbas Mahmud al-Aqad, who criticised the historical and traditional view whilst defending Islam against criticism from the West, and rejected a clear and authentic ahadith in all the books of Hadith, seera, Islamic literature as well as the consensus (ijma') of the Ummah.
He consequently presented some spurious and weak arguments to conclude:
ٍوالأَرْجَحُ عِنْدَنَا أَنّ السَيْدَة عَائِشَة كَانَتْ لَا تَقِلُ عِنْدَ زِفَافُهَا إِلَى النَبِي عَلَيْهِ السَلَامِ عَنْ الثَانِيَةَ عَشْرَةَ وَلَا تَتَجَاوَزُ الخَامِسَةَ عَشْرَةَ بِكَثِير
"ًWhat is more probable according to me is that A'isha was not younger than twelve years old nor older than fifteen years old when the Prophet consummated the marriage." (Al-Aqad, Bint as-Sideeq, p. 47)
Other Muslim writers adhered to his views such as Taha Jabir al-Alawani, Ali Gomaa and others.
This is also adopted by some recent television presenters and writers such as Adnan Ibrahim, Islam al-Buhiry and others.
Conclusion
It began with the criticism presented by David Samuel Margoliouth (d. 1940) in his book "Mohammed and the Rise of Islam" published in 1905 and spread with literary writers seeking to respond.