When I visited their apartment, the couple was right in the middle of an argument.
Tip: 真っ只中（まっただなか）is completely interchangeable with 真っ最中（まっさいちゅう）.
You can also omit 真っ and simply say 議論の最中だった. 真っ adds the nuance of “at the VERY moment”. Please keep in mind that you cannot say 議論の只中だった. I don’t know why but we don’t omit 真っ from 真っ只中.