The original Mewtwo, created by team rocket (First Movie & Mewtwo Returns), was a male.
This is the moody Mewtwo you know best.
The second Mewtwo appears in Genesect and the Legend Awakened and is female.
There is no real evidence for exactly who created this Mewtwo, but it may have been another team following Giovanni's original plans. It could also have to do with the "multiple parallel universes" mentioned to exist in ORAS.
If this were to be the case, this Mewtwo would have been created at abut the same time in about the same circumstances, but was born a female and may have never met Ash.