Joker: 5 Theories That Actually Improve It
3. Thomas Wayne *IS* Arthur Fleck's Father
One of the central points of the movie is Arthur Fleck's parentage. At the beginning of the film, we see that Fleck is caring for his mother yet we don't see a father. In fact, the only mention of a father comes later on, when Fleck reads a letter from his mother, Penny, addressed to Thomas Wayne. This letter reveals that Wayne is Arthur Fleck's father and that Thomas Wayne covered up his parentage to avoid a scandal. This also implies that Bruce Wayne and Joker are half brothers!
However, we later hear Thomas Wayne's side of the story. It is revealed that Penny Fleck had severe mental health issues and adopted Arthur Fleck, before then deluding herself into believing Fleck is her and Thomas Wayne's love child. Additionally, it's revealed that Penny Fleck was admitted to Arkham Asylum, where she was treated for delusions and schizophrenia.
While some may believe that this is proof that Batman and Joker are not half brothers, you may not want to totally believe Wayne's story just yet. Firstly, Thomas Wayne is not shown to be a good man in this movie. He is not the friendly and honourable family man that he is typically shown to be in other incarnations. In this movie, he is shown to be unforgiving and heartless and it would be in his interest to lie about his parentage of Arthur Fleck.
So, it would not be outside the realm of possibility that he cover up this pregnancy to such an extent that records are forged at Arkham Asylum. Further, both Arthur Fleck and his mother share certain psychological traits, such as delusions and wild imaginations, so it would be a big coincidence, if he was adopted, that he would also share these traits with his adopted mother.
According to this idea, Fleck's mother could have also had these mental health issues and been taken advantage of by Wayne.