Not a real doctor

Freud wasn't a genius, not even very talented.  But, the problem wasn't only Freud's lack of talent, rather It was the fact that he was much more interested in sexual escapades and cocaine than in studying, as a result, not having learned enough to be a medical practitioner.
Freud was never a real doctor. He was an imposter with a doctor's degree obtained thanks to academic fraud. Academic fraud was Freud's method of achieving success in life, starting already in high school; this is how he received excellent marks in his graduation.
He repeated the same procedure at the university, obtaining a doctor's hat, as his just (?) reward for sexual services to his gay friends having positions at the university.
Freud could hide his incompetence from his patients, but he could not hide it from his German boyfriend, doctor Wilhelm Fliess, who, almost from the start of their relationship, considered Freud a dilettante, which he pointed out to him in their correspondence. And Freud wasn't hiding his medical incompetence from Wilhelm, either.

Not learned enough

Thus, In the letter of August 29, 1888, Freud confessed to him that he, indeed, was not a doctor.
I have not learned enough to be a medical practitioner, he wrote, and in my medical development there is a flaw which later on was laboriously mended.
What kind of flaw he's talking about, and whether it was mended, is anyone's guess. Further, Freud mentioned the severe limitations of his talents, explaining that he, was able to learn just about enough to become a neuropathologist. (1)
Even though he had no idea how to treat patients - Freud wasn't a general practitioner - Freud opened a medical practise, misdiagnosing, poisoning, and even killing patients with his cures.

Dilettante

As it is apparent from Freud's response in the letter to Fliess, on May 21, 1894,  the latter sent him a letter, with the meticulous refutation of my fantasies that are typical of an intern and a dilettante. (2)
Without a doubt, Wilhelm was highly critical of Freud's pseudo-medical ideas.

I am not a doctor

Only a few months later, on August 29, 1894, Freud wistfully wrote, I wish I were a "doctor, as people say, a physician and a great healer  ... Unfortunately I am not a doctor, as you know. (3)
Now we all know.  Not a real, but a fake, doctor with a license to kill rather than to heal.  

How Freud became a "doctor"

Freud wasn't hiding how he conducted his studies.
I was decidedly negligent, he wrote, in pursuing my medical studies, and it was not until 1881 that I took my somewhat belated degree as a Doctor of Medicine. (4)
Somewhat belated? It took Freud no less than eight years to receive his diploma, rather than the more normal five.

Loafer

No wonder that, his acquaintances regarded him as a loafer and doubted whether he would get through. (5) But how did he manage at all to become a doctor?

Learned nothing

Freud befriended one of the gay professors at the university, Ernst von Fleischl-Marxow, who, thanks to his position, let Freud pass exams even without any knowledge about the subjects. As Freud recalled, during his final exam, In pharmacology ... [he] could not avoid giving the impression of having learned nothing. (5)

Somehow earned an "Excellent"

Freud was no more knowledgeable in other subjects, but it didn't matter, since, As Jones pointed out,
The first [exam], in chemistry, botany and zoology, was held by his friend Ernst von Fleischl-Marxow. ... Freud had little aptitude for chemistry; when it came to botany he failed to identify a simple flower. However, he somehow earned an “Excellent”. (5)

By the grace of the examiners 

Unashamedly, Freud himself revealed his failures in his dream book, writing, I myself failed in Forensic Medicine in my Finals; I went in for the examination in these subjects (Botany, Zoology or Chemistry) with well-founded anxiety; but, whether by the grace of destiny or of the examiners, I escaped punishment. (6)
As Jones revealed, Freud passed the exam only thanks to Fleischl's willingness to engage in academic fraud.
(1) Freud, The Complete Letters of Sigmund Freud to Wilhelm Fliess, 1887-1904, (1985, p. 23).
(2) Freud, (1985, p. 73).
(2) Freud, (1985, p. 95).
(4) SE 20, p. 10.
(5) Clark, Ronald, W., Freud, the Man and the Cause. (1982, pp. 47-48).
(6) SE 4, p. 275.